Heiko Tietze Scrabble is an open source version of the table top classic. Play with up to four players, human or computer, on a single PC or over a network.
This game doesn't require installation, which is nice, but it's not a very attractive version of the game. Heiko Tietze Scrabble is very functional in appearance, which may not reduce your enjoyment, but does mean it looks pretty outdated.
The game itself comes without dictionaries, but they can be downloaded from the developers site. However, these are not professional dictionaries, and seem to include some collections of letters that don't appear in traditional ones! You can edit dictionaries, either by adding words as you play, or by opening the dictionary file in a text program and editing it manually. Despite that option, you'll no doubt miss a professional dictionary. This is annoying if you play the computer, and it uses a word from the game dictionary that's incorrect!
Playing two or more human players, is much better, as you can agree on words as you would with the original game. One advantage of Heiko Tietze Scrabble is that you can save games and return to them later, which is much harder to do with the physical game!
Heiko Tietze Scrabble is a functional version of the game, which suffers from a poor dictionary, but otherwise does the job very well. You can keep it on your USB thumb-drive too, as it doesn't need installation.