I have a new addiction on my phone - Word Feud. Okay, it's not that new, but I still love it. A game in the style of Scrabble, you can play with friends or against random opponents. I am a geek you see. I love to play word games and other mentally challenging games (I really love a "board" game that I have called Mindtrap. My husband doesn't enjoy it, but it is such a great game that causes you to push the limits of normal thinking and think outside the box.)
What is nice is that you don't have to give the game constant attention. You can actually take up to 72 hours after your opponent's turn to play your next word. I have had games with some friends take as long as two weeks to complete.
My son recently got an iPod Touch and now plays games against us and some friends. This can be a great way to build his vocabulary. Whenever someone plays a word that he doesn't know, we have him look it up in the dictionary. I have also asked him to check a word in the dictionary if he is not sure that it is a word before playing. Now, he has attempted to play words adjacent to other words and found some two letter words that are accepted by the game, but not necessarily words that we know or would use.
I know that there is a free version of the app available for iPod, iPhone and the Droid. That is what we have. I have to deal with advertisements, but they don't bother me that much.
Speaking of free games for the Droid, iPad, and iPod, we have another game that we thoroughly enjoy and find challenge in - Unblock Me. In this game, you have a red block that you need to slide out an opening on the side of the board. The other blocks that are blocking it in can either move left and right or up and down depending on their orientation. This is a very spatial type of game that you either love because of the challenge or find frustrating. My kids like to play it a lot - although, my four year old generally asks me for help. She's still learning, so I help her out and have her watch what I am doing.