avigor: I haven't played for years, but I do seem to recall there being some difference when you get to the elven city depending on whether you are an elf or not. Are there any other major points where you race can make a quest available or block one completely?
Also, do any of the default backgrounds have any potential to make quests available or not, other than influencing your skills?
The only one I can come up with offhand is on the Isle of Despair. The dwarf who runs the encampment absolutely hates gnomes — it was a fight with one that got him exiled to the penal colony in the first place — so he will absolutely refuse to accompany a gnome PC off the island, opting instead for you to tell his clan where he's been. (And I think even this can be bent if you've gotten your CH up to 20 before you speak with him.)
There are possibly others; I'm not sure whether a half-orc can get both the good and bad options for the Donn Throgg quest, for example. But if so, they are very few and far between, and often have a workaround: for example, a woman can't enter the Tarant gentlemen's club (to research a robbery and pick up another tangential quest). Unless, of course, she's willing to sleep with the owner of the club in order to earn an exception.
As far as backgrounds go, the only one that might stop you is Technophobia; if you can't even pick up tech items, it may not be possible to complete some of the tech skill mastery quests. (Even Magick Allergy allows you to carry magic items around with you; just not to wear or equip them.)
As far as the elven city goes, the only difference your race makes is in how the guards and other NPCs greet you. All quests there are available to all races. Even dwarves.