My kids both have Leapsters (my son got his when he was 4 and my daughter when she was 3) and they both love them. They play them all of the time. I love that the games are all educational. The difference between the Leapster and Leapster 2 are that with the Leapster 2, you can have expanded play on some games and the parents can download the information to see what their child is learning, plus there are some online features as well. (We just have the original Leapster.)
My son is in first grade and this year we decided to upgrade him to the Didj. It's similar to the Leapster but the games are geared for the older kids from ages 5 to 10, up through grade 5, I believe. While the majority of the Leapster games stop at grade 2.
They do take batteries, but the great thing is that we rarely replace them. Somehow, they just don't seem to drain the batteries. The cartridges are small and easy to lose, so you'll want to either get a case to store them in. My friend has 3 kids and they all have Leapsters, so she keeps the games in her room in a box and then "checks out" the games to her kids. They can't get a new one until they've returned the previous game.
The Didj is new to us, but our neighbor boy has one and his mom said it is similar to the Leapster, just more challenging games. I have no complaints about the Leapster. We've never had a problem with either of ours and they are tough and put up with being dropped multiple times. I highly recommend it. (BTW, a friend of mine bought the V-Smile for her daughter, and within six months had replaced it with the Leapster which her daughter loves.)