>>Sorry if this is too rinky dink a question for y'all's awesome knowledge, but I figured I'd ask anyway.
>>I want to change a bike from a 16 rear 18 front (rims) to a 18 front 18 rear.
Like they said in school the only bad question is the one you don't ask.
The key to look at here is the overall height of the rim/tire assembly. The 18" tire may have a lower profile than the 16" one so the difference may be less than the rim size.
Swapping out the rear will have less of an effect than changing the front but with no other changes you will have a higher rear ride height which would result in less steering trail which would tend to make the steering feel faster.
If it is a twin shock rear bike you could find slightly shorter shocks to compensate and keep the bike in the same front/rear ride height. Mono shocks are more difficult to do this with but some do have built in ride height adjustment which would come in handy here. You could also drop the forks in the triple clamps but then the entire bike will be higher, may be good, may be bad depending on how tall you are!
Whatever way you go, definitely start slowly and see how differently the bike is behaving so you don't go flying off and hit a car or tree.
This is also a good reference for bike geometry: http://www.tonyfoale.com/Articles/index.htm
Chip in and help!