Playing with the sort of people that memorize lists of Scrabble-legal two-letter combinations (there really ought to be a name for these people... Scrabble obsessives? Scrabble maniacs?) can be difficult for the non-memorizers. One variation that eliminates this particular advantage is the no-two-letter-words rule. Of course, since two-letter word formation is often the fastest way of adding a new letter to the grid or reconfiguring a grid, eliminating two-letter words can slow down the game. It's also surprisingly challenging. When playing against beginners, I sometimes self-handicap by not allowing myself to use two-letter words.
Must-contain-an-N-letter-word is also an interesting change of pace. Variations that slow the game down may not be ideal for games of two or four players, but when you get up to six or more players, it seems that winning depends a lot more on what set of letters you get (and what order you get them in). An additional rule to balance things out may be a useful thing to have on hand.
My favorite variation on a variation is no-two-letter-nouns. This eliminates most of the letter-combinations that nobody but the memorizers have heard of, while allowing the game flow permitted by common two-letter words. (I would exclude from the exclusion two-letter pronouns. Because I like HE, IT, and ME.)
But I have some crazier ideas for variations which I intend to try out. Stay tuned...