Boggle is the second most well-known word game after Scrabble.
Of course, just because something is well known doesn't make it the best. There are any number of word games on the market that some people enjoy more than Scrabble, such as WildWords and Buy Word, but are less well-known owing to a) the stranglehold Hasbro holds over the toy market and game shelves in America, b) the name brand factor: adults buy the games they know as presents for kids, as well as other reasons.
It so happens that Scrabble is a pretty good game; I can't compare it to its competition having never played them. And Boggle is, too.
There are two main versions of the boggle game: regular and "big".
In regular Boggle, you have a tray with 16 cubes, each of which has one letter on each face. The tray is covered with a plastic lib and the entire apparatus shaken noisily. The cubes then fall (with a little prompting) into the tray spaces and the tray is uncovered.
A sand timer gives each player three minutes to find and write down as many words as he or she can in using the letters in the tray. Words can be found starting at any face and moving one letter at a time either up, down, sideways or diagonally, with the caveat that the same letter cannot be used twice, and you cannot jump over cubes. Plurals and variations of the same words are permitted. The minimum length word is three letters.
When time runs out, players compare word lists. Any word appearing on more than one list is crossed out. For the remaining words on your list, you score points for the length of the word, with progressively more points the longer the word.
The game has many great things going for it: it is lightning quick, plays equally well with almost any number of players, the rules are simple, and the game is fun. Finding interesting words in a scrambled tray of letters is an "aha" experience, which other games would do well to duplicate.
It has a few things against it, of course. It makes an awful racket when you shake up the letters. People with "Scrabble" like vocabulary are always going to wipe the floor with other players. And it requires pen and paper.
I never found a solution for the first problem, but I have worked around both of the other problems in my time.
For varying levels of skill, you can permit the better players to only listing four or even five letter words or greater. Alternatively, you can give them less time.
The pen and paper issue is probably not a problem for most people, but it is a slight drawback for me in that I can't play the standard game on shabbat (when writing is not permitted). To get around this, we played a simple "round the table" version, where each player called out a word. If you couldn't call out a word that was already said, you were out. Play continued until all but one player was out, who had to call out a final word or the game was a tie.
One story about this variant: I once played shabbat Boggle with a Haredi woman, a neighbor of mine, and the only words I could see on my initial pass were sexual slang words. She thought I was having a hard time coming up with words, but I was actually having a hard time not blurting out the words that I saw.
Big Boggle is almost the same as regular Boggle, except that the tray holds 25 cubes, the minimum length of letters in a word is four, and you have four minutes to find words.
Boggle Jr is nothing like neither of these and is to be avoided. It's an annoying early learning tool where you have to find the letters on a cube and match them to a card. There were also at some points a Boggle Bowl (buckets of dice and anagramming) and Body Boggle (like Twister with a Boggle grid.
I used to play online for free at games.com, but they no longer have a free version (you can buy one from them for $20, however). There are several other downloadable or electronic versions you can buy.
As of today, you can still play online for free at WEBoggle. Unfortunately, it can be hard to compete against people using the online Boggle Solver.
On Wikipedia. On Board Game Geek.