I like playing word games for fun rather than competitively. So I like the general idea of Scrabble®, but I don't much enjoy playing it with devotees of the game; they tend to score lots of points by playing dozens of two-letter words that nobody except The Official Scrabble Players Dictionary has ever used. (I mean, this is the dictionary that purportedly lists "aarrghh" as a legitimate word. Give me a break!) To me, the ideal word in Scrabble and most other word games is one that's obscure enough that not everyone would think of it, but not so obscure that none of the other players have heard of it. (One friend of mine has a habit of playing words that fit those criteria and happen to be seven letters long; it's a great deal of fun to watch him play, but rather frustrating to play with him if you were hoping to win.)
To underscore the fact that I'm not taking the game very seriously, I like playing silly Scrabble variants. Here are brief rules for some of my favorites:
Multidirectional Scrabble: Words do not have to read left-to-right or top-to-bottom; they can also read right-to-left or bottom-to-top. This approach (like other variants here) plays havoc with the carefully placed bonus squares on the Scrabble board, but if you're not keeping score, who cares? (For a four-player alternative variant, each player sits at one edge of the board, and plays words that read left-to-right or top-to-bottom from where ta is sitting (so that some of the letters are sideways and some are upside-down from each player's perspective). Note that the Scrabble tiles are not precisely square, so they may not fit sideways on the board as well as one might wish.)
Wraparound Scrabble: the left edge of the board is considered adjacent to the right edge, and the top adjacent to the bottom. The bonus squares at the corners of the board provide ridiculously high scores in this variant. Can be combined with Multidirectional variants.
Multi-Source Scrabble: Standard dictionaries and rules about allowable words are kinda stodgy. For more variety in words, decide that you can legally play any word that you can find easily (if challenged) in any book in the room. This gives a decided advantage to the home team, of course, and probably ought not to be played in libraries. Especially entertaining if the host has plenty of foreign-language books, science fiction books, or slang dictionaries.
Stackable Scrabble: As part of playing a word, you can stack a new letter tile on top of one that's already been played, as long as everything on the board is still a legitimate word. (Alternatively, you can swap a new letter tile for an old one, taking the previously played tile back into your hand.) You get points for every new word you create, just as in the standard game. You can even play a single tile to change an existing word without placing a new word. I think there's at least one commercial game that's designed to be played this way, but it can be played just as easily with a standard Scrabble set.
Plausible Scrabble: When a particularly silly game is called for, allow any word that sounds like it could be an English word, even if it's known not to be. "Grum," for instance, or "edgerly," or "smeffish." (For a slightly less silly version of this, allow any word or phrase that the player can convincingly define.)
Finally, you can play a similar game (without a board) called IPA Crossword, using the International Phonetic Alphabet, with a Magnetic Phonetics set from Cascadilla Press.
Scrabble is a registered trademark owned in the U.S.A. by Hasbro, Inc., in Canada by Hasbro Canada, Inc. and throughout the rest of the world by J.W. Spear & Sons, PLC, a subsidiary of Mattel, Inc. Aren't you glad to know that?