I found a new game recently, and it happens to run great on the Nokia E71. It's called Tankzors, and while it is a Java game, it's incredibly cool, and really addictive. It's pretty simply, really: you drive around (you're a tank) and blow stuff up. You sometimes have to blow up other tanks, and other times you have to blow up walls or other obstacles. Along the way you can pick up powerups, which can give you better guns or strong shields, too.
The gameplay consists of a series of missions, each one adding something different to the mix. Since most of the game is played using only the d-pad and the left and right softkeys, it works pretty well playing on the E71. Of course, the regular number keys offer shortcuts to various actions, but overall, it's a pretty easy game.
You can download Tankzors here for free, or you can just visit wap.tankzors.com from your phone. There's also a map editing tool available, if you're a bit more technical-minded and want to make your own maps.