Statutes of Limitation - There are several different statutes of limitation not here listed and some notice requirements in certain situations such as insurance claims, claims against cities and worker's compensation claims, etc...  Also, these statutes can be extended or "tolled" by disability, minority, absence from the state, discovery of the claim, etc...

Texas Civil Practice & Remedies Code

§ 16.003 Two-Year Limitations Period

(a) Except as provided by Sections 16.010 and 16.0045, a person must bring suit for trespass for injury to the estate or to the property of another, conversion of personal property, taking or detaining the personal property of another, personal injury, forcible entry and detainer, and forcible detainer not later than two years after the day the cause of action accrues.

(b) A person must bring suit not later than two years after the day the cause of action accrues in an action for injury resulting in death. The cause of action accrues on the death of the injured person.

§ 16.004  Four-Year Limitations Period

(a) A person must bring suit on the following actions not later than four years after the day the cause of action accrues:

(1) specific performance of a contract for the conveyance of real property;

(2) penalty or damages on the penal clause of a bond to convey real property;

(3) debt;

(4) fraud; or

(5) breach of fiduciary duty.

(b) A person must bring suit on the bond of an executor, administrator, or guardian not later than four years after the day of the death, resignation, removal, or discharge of the executor, administrator, or guardian.

(c) A person must bring suit against his partner for a settlement of partnership accounts, and must bring an action on an open or stated account, or on a mutual and current account concerning the trade of merchandise between merchants or their agents or factors, not later than four years after the day that the cause of action accrues. For purposes of this subsection, the cause of action accrues on the day that the dealings in which the parties were interested together cease.

§ 16.065   Acknowledgment of Claim

An acknowledgment of the justness of a claim that appears to be barred by limitations is not admissible in evidence to defeat the law of limitations if made after the time that the claim is due unless the acknowledgment is in writing and is signed by the party to be charged.

§ 16.067 Claim Incurred Prior to Arrival in This State

(a) A person may not bring an action to recover a claim against a person who has moved to this state if the claim is barred by the law of limitations of the state or country from which the person came.

(b) A person may not bring an action to recover money from a person who has moved to this state and who was released from its payment by the bankruptcy or insolvency laws of the state or country from which the person came.

(c) A demand that is against a person who has moved to this state and was incurred prior to his arrival in this state is not barred by the law of limitations until the person has lived in this state for 12 months. This subsection does not affect the application of Subsections (a) and (b).