When I look back at all the Batman games that have come and gone, THIS is the title that stands out as the best.
It isn't a very challenging game, but it's boatloads of fun! The atmosphere of the show it's based on is conveyed extremely well and everything that makes Batman Batman is found inside. Hand-to-hand combat, cool gadgets, puzzle solving, etc. The levels are nice and varied, and present lots of gameplay diversity. There's "beat 'em up" style levels, platforming levels, a driving level, puzzle solving levels...
Long story short, if you're looking for a pre-Arkham Asylum era game that makes you feel like Batman, this is it! Great graphics, great music, great gameplay... you can't go wrong!