Racial abilities from memory:

Night Elf - Star(something): Channeled spell which wasn't broken by line of sight. I have terrible memories of NE priests in BGs just spamming this on me from the roof with nothing I could do to counter it.
Undead - Devouring Plague: Pretty much the same thing although I think there was some kind of stat debuff associated with it too.
Troll - Shadow Ward: Lightning shield but with shadow orbs and a cooldown.
Human/Dwarf (I can't remember which had what)- Desperate Prayer: Same thing it is now but much weaker and I think a more substantial mana cost/cooldown.
Blood Elves - Mana (something): They channeled it and got mana back. This was back when Blood Elf racials were completely ridiculous. Spam 3 mana taps on the target then use mana torrent to silence the target and get mana back equal to the stacks you applied.
Draenei - Actually can't remember this but I know it wasn't Gift of the Naaru...or was it? This was back when certain classes had certain versions of heroic presence so I don't recall. Most draenei were rolling shaman anyway.

Humans had feedback, which was a mana drain when they hit someone in melee.
And Dwarves had Fear Ward, which was why most Alliance raiding guilds required raiding priests to reroll Dwarf.

Horde guilds didn't have that drama, since our Priest Racials weren't that great for PVE.

WoWWiki still has a page listing the old priest racial spells here:

http://www.wowwiki.com/Priest_racial_abilities

Night elves had a dodge buff and an arcane damage spell

Humans had feedback (which was kind of like a Mana Burn weapon imbue) and Desperate Prayer.

Dwarves had Desperate Prayer and Fear Ward.

Draenei had a mana regen ability (which as I understand it, eventually became Hymn of Hope), later nerfed to Chastise, and Fear Ward.

Forsaken had Touch of Weakness, an on-next-melee ability (which is to say, something you were unlikely to use once you got your first wand), plus Devouring Plague.

Trolls had a hex, which was like Touch of Weakness only without having to melee, and their shadowy version of Lightning Shield (which for a while actually displayed with a bright blue and white ball orbiting the priest.)

Blood Elves had Touch of Weakness, and... something else. Not Mana Tap/Arcane Torrent; that was something every blood elf had, not just priests.

@David73:
Oh yeah, those are the upgraded ones that came out around Burning Crusade, I think.
Feedback really did have a melee (as in, the priest had to melee) requirement back in the day, though.

they took starfall away and gave it to druids, the saddest day....

of course, in wrath we had holy nova at like 20, now its at 61, which kinda blows. I did the anathema quest on an alt finally, one i've been playing around with for years, and didn't have holy nova, had to spec disc and make the skellies hit me and kill themselves, because i had no aoe and i forgot holy water.

Consume Magic was the other BE Racial. It dispelled a both on YOU to give you a piss poor amount of mana back that was usually less than the amount of mana spent to cast the buff!

@venduer

The priest racial was StarSHARDS, and it was totally different then StarFALL.

Yeah, the Feedback racial was really stupid. It didn't help that our Inner Fire buff added attack power (I kid you not.) Oh, and it only lasted 3 minutes. Still, IF was the one thing that convinced me to start leveling my priest again - I tried rolling a pally because I was annoyed how weak my priest was. Getting IF at level 12 made a huge difference.

I liked questing, but hated leveling. Thanks to Feedback and Inner Fire, I thought I was supposed to melee stuff. Cue noob priest running around Stranglethorn Vale whacking mobs with a stick like a moron. >_< And speaking of STV, I tried with no avail to get people to group with me. I practically begged General for some help, saying I could make it go faster by reducing down time, but no, no one wanted to group. That is, until I hit 50 and could do BRD. Then suddenly EVERYONE wanted to be my friend.

@eregos.

i was being kinda sarcastic, but the abilities really aren't that different, starfall is like a beefed up version of starshards, and they got it at the same time as my priest lost her racial.

calling them both starfall was an attempt to draw a parallel between the two abilities.

@vendeurfrancais
Funny that you mention that, because Starfall was an ability belonging to the Priestess of the Moon in Warcraft 3