You can get a lot of ideas on this if you type the words 'ipad games adults' in a search engine - this will take you to lists of most popular or critically praised iPad games.
Generally, Angry Birds is still considered one of the easiest and most addictive of all games, popular with adults and children alike. There are a lot of different versions now - Star Wars is one of the best.
Another old favourite that is still well loved by adults is Dungeons and Dragons. There have been many, many games based on this - a new and popular version is Baldur's Gate, specially adapted for the iPad.
For something more puzzle based, you could try Carcassone, a strategy game something like a board game, or for sports fans there is FIFA 13. Grand Theft Auto is another famous game that is continually being updated and improved.
These are just a few ideas - you can find a lot more here.