There is one folder of games that never fails me. It is the "Story games" folder, and it contains every Kairosoft game we own:
Hot Springs Story
Mega Mall Story
Game Dev Story
Grand Prix Story
Oh! Edo Towns
If I remember rightly, this is every one they've put out on iPhone except the soccer one - Pocket League Story. So for completeness' sake:
Pocket League Story
Kairosoft has made a name for itself by making a new (to me at least) genre of games that at their core involve building stuff, unlocking new stuff to build, earning money, and expanding your empire. They fall into two main categories.
Hot Springs Story, Mega Mall Story, Oh! Edo Towns, and Venture Towns are all pretty similar. You start with a set number of buildings, build them, and try to earn lots of money and attract customers/residents as you unlock more buildings and stuff. Pocket Academy is along the same lines, except you are building a high quality school, so it has added things like tests, clubs, and field trips. All of the games have combos where you get bonuses by putting certain combinations of buildings next to each other. It becomes a challenge to get the most combos in the smallest amount of space, stay in the positive for income, and grow as fast as possible. Each game goes for 15 "years", which ends up working out to around 4-5 hours of game play (I've never timed it, but that's a rough estimate), depending on how much time you spend in the menus micromanaging.
Game Dev Story and Grand Prix Story (and I believe also Pocket League Story) are slightly different. In these games, you start as a manager of a terrible team producing low quality products (video games, racing cars, and soccer teams, respectively) and you have to work to build up your team and create better quality products to win better and better awards/recognition. These games are also 15 in-game years, if I remember correctly, and they take about the same amount of time per game. These games involve less micromanaging, but they also involve risking an investment on creating a new product (car/game/whatever) that might be completely terrible.
Both categories are excellent. I have played each of these games (except Game Dev Story for some reason, must get on that, and of course Pocket League Story) through all the way (sometimes twice) and I still find them fantastic. There's a bit of a learning curve for them, but once you've played one from each category, the rest are easy to pick up on. There are still changes between them, but the core mechanics are pretty similar, which is nice because there isn't much in the way of tutorials to teach you how to play the first time. (That's why I had to play some of them twice... once to learn how, and once to kick the trash out of my first high score.)
The easiest one by far in the first category to start with is Mega Mall Story. This one is a bit more streamlined and introduces new concepts one at a time to make it easier to learn how to play. Once you have mastered that one, moving to the others is cakewalk. Oh! Edo Towns and Venture Towns are pretty similar (I honestly could not tell much difference at all in the game play) but the others each have unique bits to them that make them just different enough to make them worth playing. Even though they are essentially all the same kind of game, they're addicting, so the little changes are enough to make it fun to play the next one.
Of them all, I think my favorite is Pocket Academy (it is the most complex but the most fun to me), but Mega Mall Story and Grand Prix Story are also high up on my list. Grand Prix Story was the one that I was sure would be stupid, and then I proceeded to play it for most of the drive to California over Thanksgiving weekend... it definitely was a pleasant surprise.
All of these games are generally going to run $3.99 each for iPhone. While I think buying a few at that price is worth it, note that you can usually snag them at $1.99 if you have patience (Venture Towns is $1.99 right now, for example). They often discount their last release when a new one comes out (again, case in point: Pocket League came out, Venture Towns is discounted) and two bucks for one of these games is well worth it.
Kairosoft's games will make a great addition to your handheld touch device. I believe most of them are currently available on both iPhone and Android (and Android might actually have a few more, like World Cruise Story... and Epic Astro Story... what! I want! ...but they do run a bit more price-wise, up to $5).
So what are you waiting for? At least go try a demo!