Well, I got into an argument about that very topic. A coworker asked me if I knew what the most poisonous spider was. I immediately guessed what he thought the answer was, and I replied that it was the Sydney funnel-web and not the daddy longlegs. He then explained that yes daddy longlegs were the most deadly, just their fangs can't penetrate human skin. Well, I hadn't heard that one so I did some research (turns out it's the funnel-web from Sydney afterall, the Atrax robustus).
I did a bit of research, but not enough that I've worked out all the differences between them, but they seem to come in three common varieties: one in North America, one in Britain and one in Australia. The "proper" daddy longlegs actually occur in many other places, but nobody else calls them that. Anyway, here's what I learned.
The North American one is not a spider, though it is a close relative, and is the tamest of the three varieties. In fact, not only is it venomless, its fangs aren't even functional. Its only defense is that it can break its legs off at will and remotely wiggle them while it makes a getaway so it can regrow its legs in safety.
In the UK, daddy long legs apparantly describes an annoying little crane fly (as lj pointed out to me). The "spider" we in the States know by that name is properly called a harvestman. Pretty much the same as the US version, but this one has quite a chemical defense. Millions of years of evolution have bestowed upon it a pair of sacs on its carapace that provide one of the most infamous natural defenses: it smells bad. (The US version may actually have this defense too. I couldn't figure out from the sources whether or not these are the same species.)
Now the Aussie daddy longlegs really is a spider complete with webs, eight legs and more than two eyes. Also, like every other creepy crawly thing in Australia, it is venomous, and it does quite frequently kill or maim thousands of smaller, clumsier spiders and insects every year. There is no antivenom for those small buggy things, but fortunately, its venom (not just the spider, its venom too) is completely and totally harmless to humans.
As I mentioned earlier, there are actually more species. And they are all harmless in every way. Unless you are a really small spider or a mite or piece of rotting lettuce, you should be okay. In fact, the more I read about the daddy longlegs, the more amazed I was that this thing didn't go extinct eons ago. So go ahead and eat one today. They're harmless.