Wrongful discharge is a serious problem, as it can be indicative that an employer isn't fair to employees and may be discriminatory. There is a difference between wrongful discharge and employment-at-will rules that you should understand. Not all people who have been fired were done so wrongfully.
In Texas, employers have the right to hire or fire workers at will. Employment-at-will laws allow this to happen. Unless there is a contract in place that says otherwise, the employer has the right to end an employee/employer relationship for any reason, or no reason, without notice. The employer may choose to give notice as well.
There are some exceptions to the rule that could result in an employer being accused of wrongful discharge, though. For instance, if you were working a job and were attacked due to your race before being fired, you may have cause to claim racial discrimination as the reason for being fired. This is against the law.
In another circumstance, you may have discussed a problem on the job, like fraudulent activity. This whistleblower activity is protected under law, so you can't be retaliated against for bringing it to your employer's attention. If you're fired for doing so, you may be able to seek compensation.
Another situation you can't be fired for is having to leave for military duty. As a service member, your job is meant to be protected in the event that you have to leave the country or serve with the military in any form. If you're fired for being in the military, your employer has likely broken the law.
There are other exceptions as well, so if you've been fired, you may want to look into them. From jury duty rules to contractual obligations, your employer has strict rules he must abide by, even under the employment-at-will laws.
Source: Texas State, "Wrongful Discharge" accessed Feb. 18, 2015