Theoretically speaking, you can play Wizard101 with a dial-up connection. HOWEVER, it would be incredibly slow, choppy and make you want to cry. You'd then likely send many tickets to the support team complaining of the poor game experience, thereby driving them to tears as well.
If you have a basic cable or DSL connection - doesn't have to be the very fastest, but it does need to be stable - you should be able to play Wizard101 without issue.
