I recently learned a great game that can be played with the Bananagrams tiles. It is currently sold under the name "Snatch", but earlier versions actually pre-date Scrabble and, if the Wikipedia entry can be believed, has existed in some form since the Victorian era.
Like Bananagrams, it can be played with 2 to many players, but also like Bananagrams, it seems like (tentatively) 4 is the optimum number.
The object is simply to build words from the available tiles. Start with all the letters face down in the center of the table. One player starts turning over tiles until someone sees a combination of tiles that make a word (at least 3 letters long). They shout out the word and claim it. Then the next player starts turning over tiles. What makes the game interesting is that, even a word that have been claimed by a player can be snatched away if someone sees a way to combine all of its letters with one or more tiles from somewhere else on the table to make a new word. New words must have a different meaning. (You can't just use another form of the word. For instance, if someone has the word TONE, the variations TONES and TONED are not allowed. STONE, on the other hand, would be a legitimate snatch.) You can build off of your own words, and you can combine the letters from multiple words to form a single new one.
The rule that I really like is that, if you see a word, you can snatch it at any time. For example, Alice turns over a tile. Bob sees a word and snatches it. Your first reaction (from the paucity of options when the game first starts), is to wait for Bob to take his turn flipping tiles. But if you see a word, you can grab it immediately.
Ties: If Alice and Bob both call out words at the same time and the words share at least one tile, the conflict can be resolved by yielding to whoever has the longer word. You should make up your own house rule for when two players call out the same word (or words of equal length) at the same time. (One idea is to throw those tiles back into the pool.)
When all the tiles have been turned over, play continues until everyone decides that there are no more moves to make and quits. Scoring is completely arbitrary. I like counting the number of words, but admittedly, this penalizes for combining two of your own words to form one longer one.
You can play Snatch with Bananagrams tiles (which I call "Bananasnatch"), but you may find that there are a few too many vowels as the Bananagrams set is optimized for Bananagrams while the Snatch set is designed for playing Set. I threw out about 12 of the vowels and found that we had a pretty good game. Throwing out more may make the game steadily more challenging. I will have a more detailed analysis of the letter distributions in a forthcoming post.
After playing one round of Bananasnatch, everyone wanted to play again. It is tremendous fun! It's perfect for when you've played six or seven rounds of Bananagrams and you want to change things up a little bit.