Eric Heberling did the music for the first two installments, Arena and Daggerfall. There's a reason there are dozens of music modifications for the later games floating around that replace Soule's works with arranged versions of the tunes from those older in the series, and it's not just nostalgia.
Take a listen to Track 21. Phenomenal composition.
Track 26, the swimming theme. Gorgeous piece of music.
Check this out, an index of all specially remixed/arranged Daggerfall compositions. The ones by Dan Goodale are truly epic.
The recurring 'Elder Scrolls' theme mentioned in the Morrowind/Oblivion category? Contrary to what Morrowind's YMMV page may lead one to think, it began with Daggerfall's GSNOW_B. The Snowing rendition is not really the same song, because as you can see, the riffs from later games were put into the above remix, but you can't help but be reminded of it by either version.
"One They Fear", the remix of the main theme used as boss music, has been known to induce Theme Music Power Ups in players. Here is a song that has got many a player killed, simply because they got so pumped while it was playing that they attacked the dragon in question head-on.
"Sovngarde" is pretty awesome by itself, but when it plays when you enter the Nordic land of the honored dead to do final battle with Alduin himself with the ancient heroes at your side, it takes it Up to Eleven.
"Watch the Skies" is unbelievably awesome, especially when fighting a particularly nasty dragon.
Secunda, one of the best ambient pieces in the soundtrack. Tundra is the other best ambient piece. A close third goes to Dragonsreach.
"We are the Dragonborn of Tamriel. We come from all corners, all places. From Skyrim, Morrowind, Hammerfell, The Summerset Isles, Cyrodil and all others. We are of all races. Nord, Orc, Breton, Imperiel, Elf Kind (Wood Elves, Dark Elves and High Elves), Khajiit, Redguard and Argonian. We are born in times of extraordinary crises. Tamriel will never fall into darkness. We the Dragonborn, the Dovahkiin will rise above all evil, vanquish it back into Oblivion. Always remember: Sky above, Voice within." -Youtube Commentator
Unbroken Road. It plays once in the entire game (specifically, when the ancient heroes banished Alduin the first time), and it is awesome. For some reason, this theme did not play in the Elder Scroll sequence for this troper; instead, it played after she finished Season Unending, right before the final battle against Alduin. And for some reason, that makes it sound even more epic to this troper.
Dragonborn adds to the game a bunch of new tracks, most of which are Morrowind remixes. They are amazing. Forgotten Vale from the Dawnguard DLC rivals "Wind Guide You" in terms of its larger-than-life scope.
The Dark Reprise of the main theme used for the Dragonborn trailer is just epic. Even better, the Dragonborn DLC will feature a return to Solstheim, once the setting for Morrowind's expansion Bloodmoon. A chanting portion of the Skyrim "main theme" from the original game is a remix of the "MorrowindLeitmotif" that became recurrent in all TES games from the third onwards, including Oblivion. Guess which part of the Skyrim "main theme" turned up for the trailer? And if one listens to the lyrics they are chanting, instead of being about the Dragonborn and their heroism, these same words are now being twisted and warped to reflect Miraak's menace.