what did legolas shoot at?
 

In the river Anduin after the Company has been seen by orcs, a dark flying creature approaches them. I first thought that it was a Nazgul and/or his "winged beast" since Frodo's old wound became cold, but then legolas shoots one arrow towards it and kills it. at least I presume he kills it because later on Frodo says that it's fall has dismayed their enemy. But surely a "winged beast" cannot be killed that easily?

Well, I can only add my supposition here; I always guessed it was one of the Crebain that Aragorn and Sam see before they go on Caradhras. They are spybirds, so one of them following the Fellowship wouldn't be unexpected. And the Enemy would definitely be dismayed that Legolas shot it down, because that means he can't spy on them until he gets another Crebain out there.

That's just my guess, though. ^_^

Actually, Legolas did shoot down the one of the Nazgul's winged steeds. I know this because Frodo's wound became cold when it flew overhead. And I can only assume that was from where the Nazgul stabbed him at weathertop.

As for how he could kill it so easily, remember that Legolas is a very good shot. He can see a lot, even though it was at night. He could have shot him through the heart, or up into his brain. Any one of the two would kill it instantly. And he probably has about an 100 pound pull on his bow that would make his arrow go in deep anough to kill it. I think that Legolas, even though he doesn't really know what it is, knows the best way to kill anything that would be stalking them.

Hmm... doesn't 100 pounds seem a bit like overkill, even for an Elf? Then again, in the Middle Ages, some longbowmen were using bows with pull weights well over 100 lbs. I always thought that Legolas's bow was something around 60-80 lbs, but I suppose that wouldn't have been able to shoot an arrow that high and that accurately, unless he overdrew a lot.

Legolas said to Gandalf later on that he shot a dark shape out of the sky and Gandalf said that it was a winged steed of Nazgul. That pretty much clears up the doubt, I think. Olorin would be scarcly wrong.

Hmmm... I can't remember this part in the book. I really have to read them again. I will put it on my to do list.

ya i think that legolas killed the the nazguls flying beast
the first reason for this is that frodos old wound hurt and started getting cold
and i remember gandalf telling legolas that shooting the beast was a good deed but only the flying beast was killed and the the nazgul was soon horsed again.

Is this what you guys mean?

Which also brought the question: How many "winged steeds" did Sauron breed? Surely, if there are more than enough of them to re-horse a Nazgul, there would have been enough to horse other of his servants?

True, but the Nazgul were the only ones who really needed the winged steeds, since they were Sauron's messengers. Sauron doesn't come across as a wasteful person, so he probably only "made" enough for the Nazgul, and didn't plan to let any of his other servants use them.

English war bows typicly had a draw weight of 140 to 160 lbs, i emagine Legolas, being an Elf, could have pulled that without much strain, 130 lbs would rip through metal plate armor and 160 would most likely rib througn the body of one who had armor on.

i think that the body of a winged steed would probably be equal to that of steel plate armor(if not greater) so adding the height, and gravity, a 150 lb bow would probably kill it.

It's simple: Legolas is described as being immensely strong by Tolkien, it was given him a "great war-bow"(the most ranged bow in all middle earth made in Lórien and would weight a lot), great sight and steady hands.
The arrow probably stuck to deep in the Nazgul flesh(who isn't as dense as ancient Dragon for example).

His first bow was like that and came from Mirkwood but later Galadriel gave him one of the Lorien bows which are very long and weights a lot.

Uglúk confirms
 

Another confirmation that Legolas killed (or at the least downed) the steed comes in the chapter The Uruk-Hai in 'The Two Towers.' As the Orc factions quarrel on the night before the Rohirrim attack, Uglúk of Isengard taunts Grishnákh of Mordor: "What's happened to your precious Nazgûl? Has he had another mount shot under him?"