When I say that the gameplay has aged, I don't mean that Fallout is unplayable. It's still great fun to play, but you'll encounter issues that are less forgivable in modern games, like the inventory menu, or your allies constantly blocking doorways. The high points are the story and the character customization, two things that Fallout still does better than most RPGs today. You can blast your way through the game, or you can beat the game without killing a single thing (though I don't recommend this on your first playthrough, since combat, while technically optional, is a pretty large portion of the game).
Side note: Ever notice that some of the best computer RPG systems are based on pen and paper ones? There are a number of fantastic D&D games out there, like Baldur's Gate, Icewind Dale, and Neverwinter Nights. The influence of pen and paper roleplaying on Fallout is strong - the developers intended to license the GURPS system, one of the better pen and paper games out there, but when they failed, they developed their SPECIAL system instead, which in my opinion is a great mix of the best of tabletop RPGs and computer RPGs. This influence also explains Fallout's devotion to character and story over gameplay, and its excellent integration of numerical stats into a believable character (with a couple exceptions: obviously increased gun skills should improve accuracy, but the fact that they also improve damage, while good for gameplay, isn't as realistic as it is for melee weapons).