More of the same?
Crystal is a "remake" (or better, an improvement) of Pokemon Gold and Pokemon Silver. It contains almost all the features of these games but it comes with new areas to explore and new stuff to acquire, and generally just new things to do. In fact while the storyline is pretty much still the same, there are new characters and new events absent in the original games. Among these are a new rival, the Battle Tower (which will make a comeback in Pokemon Ruby/Emerald), and more.
Unlike the original game you can choose if you want to be male or female (as Nintendo realized the game was quite popular among girls). The pokemon met in the game are from both Gold and Silver, so theorically if you want to complete the pokedex you must own both Gold and Silver or have a friend who can trade the pokemons you need.
As for the game itself, if you haven't played Pokemon Gold, in this game you can visit both Johto (the new region) and Kanto (the region of the first pokemon games). In fact this game will keep you busy for much longer than pokemon red/blue, and this is indeed a good thing. The new pokemons are all as good as the original ones. They introduced some new ways of evolving pokemons, like Pokemon Eggs and pokemons that evolve if traded while they hold a certain item. You can again battle the Pokemon League and even battle the player character of the first pokemon game at the very end of the game!
On the "bad" side, while many of the flaws/limitations from Pokemon Red/Blue have been removed making the game much more user-friendly, some are still present. For example every time you want to change the box on Bill's PC you still need to save the game, which can become kind of annoying. However it's nothing really major, most of the issues of pokemon red/blue have indeed been fixed.
So anyway here's the deal: If you have already pokemon gold and pokemon silver and want a 'new' pokemon game, apart from the improvements this game is pretty much the same as gold and silver so I suggest you get something else like Pokemon Emerald (which is well worth your money). Still this is a very entertaining game and I think it's the best one in the pokemon series. If you don't own either Gold or Silver, definitively get this instead of one of these two.