Cut the Rope: Experiments ($0.99) & Experiments HD ($1.99)
This is not an elaborate or coded title. It means what it says. In the sense, all you have to do is cut the rope. The game, which has been developed by ZeptoLab is one of the only games able to rival Angry Birds in terms of popularity.

Once the user cuts the rope, which holds a piece of candy, he/she will be able to witness a cute lizard like creature named Om Nom get at it. The challenge is more difficult than you can imagine, requiring a great deal of concentration and observational skills.
Experiments is a sort of sequel and brings about 75 new levels to tease users and fatten Om Nom. The challenges are sure to get users excited. More exciting is the fact that ZeptoLab has promised a variety of new updates in the near future. Users who have played the original version and loved it should definitely get their hands on Experiments. It is worth every cent!
Puerto Rico (iPad only $7.99)
While the game traces its origins to the classic board game, the iPad version comes with a great deal of advantages for users. Users will get access to instant tutorials and help articles. In addition, a cool new multiplayer system allows you to pass and play with multiple users. You can play with up to four players.

Like all strategy games, this has a slightly higher learning curve but once you get the hang of it there is a high probability that you will become addicted to it.
The price is the only issue here but after reviewing the amount of effort that has gone into rebooting this classic, one could argue that it is actually reasonable. If you have kids at home and need to pass the time, then this is a really good game to consider.
Final Fantasy: The war of the Lions (Currently only available on the iPhone for $15.99)
Few tactical RPG games can rival the Final Fantasy series. This wonderful game developed by Square Enix features updated leveling and stats features. It also allows users to control multiple characters and face groups of enemies on a turn-based combat system. The battlefield is divided into a grid, to allow full user customization and control.

On the iPhone and iPod Touch, the game works very well. The touch screen controls are also very responsive. The only major issue is the price, which is relatively steep. However, if you want to get your hands on one of the best selling tactical RPG games on the market right now, it is not a bad price after all.