To clarify what USMCFlyer said-

As far as the FAA is concerned, once you pass your checkride you are qualified to fly any "Airplane, Single-engine Land". From cessna to piper, as long as it has one engine and can only land on terra firma, your good.

Now, insurance (the FBO's) is another thing completely. Even though the FAA says your qualified, any FBO you rent from will most likely require you to go on a check out flight with one of their CFI's. This is a requirement under the FBO's insurance and has nothing to do with the FAA. Plus is probably a good idea so that you can learn and become familiar with the aircraft with someone who is familiar with it.... ie- a piper doesn't land the same as a 172.

Good luck on the check ride. Just do what your instructor taught you (don't try to show off or try something different) and you'll do just fine!