From the Law Office of Alison Grinter in Dallas, Texas

Criminal cases can often endanger a person's legal status as an immigrant in the United States. This applies to legal permanant residents, as well as people here in the United States who would like to become a legal permanant resident or naturalized citizen.

If you have concerns about whether a criminal matter will endanger your immigration status, PLEASE, contact an immigration attorney BEFORE you enter a plea of any kind. In many cases, your criminal matter can be handled differently if your criminal defense attorney understands what the immigration judges will be looking for when they ultimately evaluate your case, and that kind of understanding can only come from conferencing with your immigration attorney on your specific circumstances.

There are some types of cases, however, which, on "conviction" (and for these purposes, "conviction" includes deferred adjudication). These offenses, called "Aggravated Felonies" by the Federal code,  even though in some cases, they can be considered misdemeanors here in Texas.

It is also notable that a sentence of probation / Community Supervision (known to the Feds as a "suspended prison sentence") counts as a term of incarceration for these purposes,

Statutes

Aggravated Felonies

8 USCS Sec. 1101 (a)(48)(B)

(43) The term “aggravated felony” means—
   (A) murder, rape, or sexual abuse of a minor;
   (B) illicit trafficking in a controlled substance (as defined in section 802 of title 21), including a drug trafficking crime (as defined in section 924 (c) of title 18);
   (C) illicit trafficking in firearms or destructive devices (as defined in section 921 of title 18) or in explosive materials (as defined in section 841(c) of that title);
   (D) an offense described in section 1956 of title 18 (relating to laundering of monetary instruments) or section 1957 of that title (relating to engaging in monetary transactions in property derived from specific unlawful activity) if the amount of the funds exceeded $10,000;
   (E) an offense described in—
        (i) section 842 (h) or (i) of title 18, or section 844(d), (e), (f), (g), (h), or (i) of that title (relating to explosive materials offenses);
        (ii) section 922 (g)(1), (2), (3), (4), or (5), (j), (n), (o), (p), or (r) or 924 (b) or (h) of title 18 (relating to firearms offenses); or
        (iii) section 5861 of title 26 (relating to firearms offenses); 
   (F) a crime of violence (as defined in section 16 of title 18, but not including a purely political offense) for which the term of imprisonment at is least one year; (G) a theft offense (including receipt of stolen property) or burglary offense for which the term of imprisonment at is least one year;
   (H) an offense described in section 875, 876, 877, or 1202 of title 18 (relating to the demand for or receipt of ransom);
   (I) an offense described in section 2251, 2251A, or 2252 of title 18 (relating to child pornography);
   (J) an offense described in section 1962 of title 18 (relating to racketeer influenced corrupt organizations), or an offense described in section 1084 (if it is a second or subsequent offense) or 1955 of that title (relating to gambling offenses), for which a sentence of one year imprisonment or more may be imposed;
   (K) an offense that—
        (i) relates to the owning, controlling, managing, or supervising of a prostitution business; 
        (ii) is described in section 2421, 2422, or 2423 of title 18 (relating to transportation for the purpose of prostitution) if committed for commercial advantage; or
        (iii) is described in any of sections 1581–1585 or 1588–1591 of title 18 (relating to peonage, slavery, involuntary servitude, and trafficking in persons);
   (L) an offense described in—
        (i) section 793 (relating to gathering or transmitting national defense information), 798 (relating to disclosure of classified information), 2153 (relating to sabotage) or 2381 or 2382 (relating to treason) of title 18; 
        (ii) section 421 of title 50 (relating to protecting the identity of undercover intelligence agents); or
        (iii) section 421 of title 50 (relating to protecting the identity of undercover agents);
   (M) an offense that—
        (i) involves fraud or deceit in which the loss to the victim or victims exceeds $10,000; or 
        (ii) is described in section 7201 of title 26 (relating to tax evasion) in which the revenue loss to the Government exceeds $10,000;
   (N) an offense described in paragraph (1)(A) or (2) of section 1324 (a) of this title (relating to alien smuggling), except in the case of a first offense for which the alien has affirmatively shown that the alien committed the offense for the purpose of assisting, abetting, or aiding only the alien’s spouse, child, or parent (and no other individual) to violate a provision of this chapter [6] (O) an offense described in section 1325 (a) or 1326 of this title committed by an alien who was previously deported on the basis of a conviction for an offense described in another subparagraph of this paragraph;
   (P) an offense
        (i) which either is falsely making, forging, counterfeiting, mutilating, or altering a passport or instrument in violation of section 1543 of title 18 or is described in section 1546(a) of such title (relating to document fraud) and 
        (ii) for which the term of imprisonment is at least 12 months, except in the case of a first offense for which the alien has affirmatively shown that the alien committed the offense for the purpose of assisting, abetting, or aiding only the alien’s spouse, child, or parent (and no other individual) to violate a provision of this chapter;
   (Q) an offense relating to a failure to appear by a defendant for service of sentence if the underlying offense is punishable by imprisonment for a term of 5 years or more;
   (R) an offense relating to commercial bribery, counterfeiting, forgery, or trafficking in vehicles the identification numbers of which have been altered for which the term of imprisonment is at least one year;
   (S) an offense relating to obstruction of justice, perjury or subornation of perjury, or bribery of a witness, for which the term of imprisonment is at least one year;
   (T) an offense relating to a failure to appear before a court pursuant to a court order to answer to or dispose of a charge of a felony for which a sentence of 2 years’ imprisonment or more may be imposed; and
   (U) an attempt or conspiracy to commit an offense described in this paragraph.
The term applies to an offense described in this paragraph whether in violation of Federal or State law and applies to such an offense in violation of the law of a foreign country for which the term of imprisonment was completed within the previous 15 years. Notwithstanding any other provision of law (including any effective date), the term applies regardless of whether the conviction was entered before, on, or after September 30, 1996

Other Deportable Offenses

8 USCS Sec. 1227(a)(2) -

(2) Criminal offenses 
   (A) General crimes
        (i) Crimes of moral turpitude Any alien who— 
             (I) is convicted of a crime involving moral turpitude committed within five years (or 10 years in the case of an alien provided lawful permanent resident status under section 1255 (j) of this title) after the date of admission, and
             (II) is convicted of a crime for which a sentence of one year or longer may be imposed,
is deportable.
        (ii) Multiple criminal convictions Any alien who at any time after admission is convicted of two or more crimes involving moral turpitude, not arising out of a single scheme of criminal misconduct, regardless of whether confined therefor and regardless of whether the convictions were in a single trial, is deportable. 
        (iii) Aggravated felony Any alien who is convicted of an aggravated felony at any time after admission is deportable.
        (iv) High speed flight Any alien who is convicted of a violation of section 758 of title 18 (relating to high speed flight from an immigration checkpoint) is deportable. 
        (v) Failure to register as a sex offender Any alien who is convicted under section 2250 of title 18 is deportable. 
        (vi) Waiver authorized Clauses (i), (ii), (iii), and (iv) shall not apply in the case of an alien with respect to a criminal conviction if the alien subsequent to the criminal conviction has been granted a full and unconditional pardon by the President of the United States or by the Governor of any of the several States.
   (B) Controlled substances
        (i) Conviction Any alien who at any time after admission has been convicted of a violation of (or a conspiracy or attempt to violate) any law or regulation of a State, the United States, or a foreign country relating to a controlled substance (as defined in section 802 of title 21), other than a single offense involving possession for one’s own use of 30 grams or less of marijuana, is deportable.
        (ii) Drug abusers and addicts Any alien who is, or at any time after admission has been, a drug abuser or addict is deportable. 
   (C) Certain firearm offenses
Any alien who at any time after admission is convicted under any law of purchasing, selling, offering for sale, exchanging, using, owning, possessing, or carrying, or of attempting or conspiring to purchase, sell, offer for sale, exchange, use, own, possess, or carry, any weapon, part, or accessory which is a firearm or destructive device (as defined in section 921 (a) of title 18) in violation of any law is deportable.
   (D) Miscellaneous crimes
Any alien who at any time has been convicted (the judgment on such conviction becoming final) of, or has been so convicted of a conspiracy or attempt to violate—
        (i) any offense under chapter 37 (relating to espionage), chapter 105 (relating to sabotage), or chapter 115 (relating to treason and sedition) of title 18 for which a term of imprisonment of five or more years may be imposed;
        (ii) any offense under section 871 [Threats against the President] or 960 [Expedition against a Friendly Nation] of title 18; 
        (iii) a violation of any provision of the Military Selective Service Act (50 App. U.S.C. 451 et seq.) or the Trading With the Enemy Act (50 App. U.S.C. 1 et seq.); or
        (iv) a violation of section 1185 or 1328 of this title,
is deportable.
   (E) Crimes of domestic violence, stalking, or violation of protection order, crimes against children and
        (i) Domestic violence, stalking, and child abuse Any alien who at any time after admission is convicted of a crime of domestic violence, a crime of stalking, or a crime of child abuse, child neglect, or child abandonment is deportable. For purposes of this clause, the term “crime of domestic violence” means any crime of violence (as defined in section 16 of title 18) against a person committed by a current or former spouse of the person, by an individual with whom the person shares a child in common, by an individual who is cohabiting with or has cohabited with the person as a spouse, by an individual similarly situated to a spouse of the person under the domestic or family violence laws of the jurisdiction where the offense occurs, or by any other individual against a person who is protected from that individual’s acts under the domestic or family violence laws of the United States or any State, Indian tribal government, or unit of local government. 
        (ii) Violators of protection orders Any alien who at any time after admission is enjoined under a protection order issued by a court and whom the court determines has engaged in conduct that violates the portion of a protection order that involves protection against credible threats of violence, repeated harassment, or bodily injury to the person or persons for whom the protection order was issued is deportable. For purposes of this clause, the term “protection order” means any injunction issued for the purpose of preventing violent or threatening acts of domestic violence, including temporary or final orders issued by civil or criminal courts (other than support or child custody orders or provisions) whether obtained by filing an independent action or as a pendente lite order in another proceeding.
   (F) Trafficking [of Persons]
Any alien described in section 1182 (a)(2)(H) of this title is deportable.