Which STDs cause urinary problems?

Difficult to say... You don't provide enough information for an accurate reply. Many STDs can cause symptoms that mimic other genital problems, like urinary tract infection. Most don't cause actual "urinary problems", but that depends on just what you mean. Can you say more about what symptoms you have had or why you are concerned?
UTI, GC and chlamydi. Dysuria, may be a sign of a regular uti, caused by bacteria like e. Coli. It may also be a sign of an std. Most common stds causing dysuria and urethritis are gonorrhea, chlamydia and possible herpes. Swabs and urine testing can find the source for you.