This issue has always come up a lot on here, and the results are always similar. If you are strictly a league bowler, you can probably get away with one or two entry-level to mid-price balls to cover all of your needs. There is a fantastic market at that price point these days. You really don't need the higher end stuff in most cases because the patterns won't have enough oil to really make them worthwhile anyhow.
Now, if you're a tournament bowler, it makes sense to have an "arsenal" of some sort because it will allow you flexibility for the different patterns you may face. The size of that arsenal is up for debate. Some people will say you need 3-4 balls, and some people will say you need 7, 8, 9, etc. I remember a feature story on Diandra Asbaty back in the day that said she routinely traveled to tournaments with more than 40 balls in the back of her SUV. She just said she just never knew whether there would be a need for a particular ball until she got there, so she always wanted to be able to grab it if she needed it. Really, it's up to the bowler. As long as you don't mind lugging the stuff in and out of the car, bring however many makes you happy.