Danny Elfman's music for the first two films, Batman in particular, is one of the very few elements of the original film series that many people think the Nolan films haven't come anywhere near topping.
The opening number, literally titled "The Batman Theme", makes the accompanying titles so awesome that you can fail to notice that next to nothing's happening onscreen. The theme gets a reprise at the film's end. It is also rescored as the opening theme for Batman the Animated Series.
"Waltz to the Death," which is what the Joker and Vicki Vale were dancing to while Batman was beating up Mooks, is also quite amazing.
"Descent into Mystery," which is heard when Batman drives Vicki Vale through the forest to the Batcave. So epic, it was reused in the trailer to Batman Returns.
The "Finale", the most triumphant piece of Batman-related music ever. Especially epic is the crescendo (before the familiar "Batman Theme" hook at the end) combined with the image of Batman standing on a ledge, silhouetted against the night sky, with the Bat-signal in the distance. If that doesn't give you goosebumps, nothing will.
In addition, the pop soundtrack composed by Prince has some pretty awesome numbers, too. The crowner is probably "Batdance", picked as the main single from the album. It was #1 on the charts for a reason, folks.
Elfman's incredibly intense score for Batman Returns is nothing short of awesome, either. Especially epic is the opening number, "Birth of a Penguin", complete with a dark re-orchestration of the previous film's theme.
The latter two films in the series may not have been the greatest, but both include pop soundtracks that are actually enjoyable to this day. At the very least, no one can deny that "Kiss from a Rose" was the single of 1995.
And while still a distant third to Elfman and Zimmer/Newton Howard's scores, Elliot Goldenthal's scores are still pretty amazing, delivering the proper level of bombast for an abjectly cartoonish universe (Goldenthal specifically chose to invoke a feeling similar to a Russian circus). Sadly, most of the music he composed for Batman Forever was shelved and unreleased in favor of the aforementioned pop-heavy soundtrack, and has only recently become commercially available in its full length.
Whilst it seems to only be on the soundtrack to Batman Begins, not in the actual movie (at least, not in it's entirety), "Lasiurus" possibly sums up the essential character at the heart of Batman better than any piece of music (even some of the other fine pieces listed here) ever will — it's dark, brooding and melancholy, and yet there's a subtle note of hope weaved in there that gradually and powerfully builds to a crescendo, giving the listener the impression that the night will end and evil will be overcome...
The last minute of Aggresive Expansion. If "Why So Serious?" builds up the tone of the Joker, this song smashes it down on you like a 5000 pound hammer. It's impossible to listen to this song without imagining him bursting into the room and holding a knife to someone's neck at the last second, and to top it all off, the scene it's used in is when he kills the goddamned judge and commissioner.
Next time you watch The Dark Knight Rises, consider muting the film as the credits begin and playing this fan-made track over them. It starts low and quiet, but builds to a final crescendo for the trilogy that simply must be experienced.