Parking tickets in Texas these days are usually not criminal matters that can result in a warrant or arrest. However, they are considered administrative matters and can hold up issuance of permits, etc. in the city where they are outstanding. You have experienced what can happen if they go unpaid - credit report "dings" and resulting inconvenience and hassles. It is generally best to just pay them, because the expense and trouble of fighting them is often not cost effective. That said, I have sometimes been able to save my clients money on the more expensive parking tickets, such as parking in tow-away or handicap zones. Consult with an experienced traffic ticket attorney if you have such questions.