If you've ever played Boggle it's clear that there's an indescribable but tangible quality that makes playing Boggle more fun than it would seem at first glance. But what is it about Boggle that makes playing so gleefully enjoyable? How can you convince your neighbor/spouse/kid to play Boggle if you can't at least explain part of why Boggle is great?
From the perspective of a long-time Boggle player, I think Boggle is fun because it changes each round, the Boggle timer keeps the game moving, and there's opportunity for conversation. Now, none of these reasons can fully account for the greatness of Boggle play as there's still an ineffable quality of Boggle enjoyment, but they're a start toward an explanation.
Boggle play changes each round as the Boggle cubes reveal different combinations of letters. Some Boggle rounds with lots of good letters have players scrambling to list a seemingly endless number of common three and four letter words. At other times the creativity of players is strongly challenged by Boggle cubes with an unfortunately high percentage of vowels, z's, and qu's. This is when unusual Boggle words like squeegie are sometimes found!
Besides changeability, Boggle's timed nature keeps players geared up and energetic. Unlike Scrabble which may bore players to tears while one person takes their turn (although I do like Scrabble), Boggle allows a limited amount of time which serves to keep Boggle players engaged and excited (much the same way that a game like Taboo does).
Finally, while Boggle is at times quiet (as Boggle players search for words), the players still have time to chat, laugh, and applaud each other's words during the second phase of the Boggle round. Thus Boggle is a fun game that makes you think, gets your energy going, but still leaves room for Boggle players to have the sense of hanging out with friends.
But that still doesn't totally explain why playing Boggle is so great...!