This is a sweet idea, so I will write some little games I used to play.

There is the 'I went to the store' memory game.

One person starts off by saying "I went to the store to buy a..." something that starts with the letter A (let's say apple).

Second person continues by saying "I went to the store to buy an Apple", and then will add their own item, beginning with B (let's say banana)

You take turns working through the alphabet to build up a list of items, "I went to the store to buy an apple, a banana, a cat, a..." You can come up with all sorts of crazy items, and see whose memory wins.

_

Take a letter of the alphabet, and within one minute (timed) the person has to come up with as many different words as they can beginning with that letter. Other player counts how many words they come up with. The next person does it with another letter. See who can come up with the most words, or most original & interesting words. I don't know if there are actual rules to this game, but that's how I remember it.

_

There's a game you can play on paper. Make about 10 rows and columns on two separate sheets of paper, one for you and one for the other player. Along the first row write the following categories (or whatever else you can think of): Boys Name, Girls Name, Country, Animal, Household object, Singer/Band, Color, Sports/Games, Fruit and Vegetable, and Total. Say the alphabet in your mind, and the other person will tell you to 'Stop' on a letter. With that letter, you both try to fill in all the categories as fast as you can. The first person who finishes them all first will say "Stop!" and then you both write in your total for that round. By the end of all the rounds, add the final total, and celebrate your victory. lol

Good luck.