Couple things here (from the 3.5 SRD)...
Opposed Checks
An opposed check is a check whose success or failure is determined by comparing the check result to another character’s check result. In an opposed check, the higher result succeeds, while the lower result fails. In case of a tie, the higher skill modifier wins. If these scores are the same, roll again to break the tie.
and
Trying Again
In general, you can try a skill check again if you fail, and you can keep trying indefinitely. Some skills, however, have consequences of failure that must be taken into account. A few skills are virtually useless once a check has failed on an attempt to accomplish a particular task. For most skills, when a character has succeeded once at a given task, additional successes are meaningless.
Also note, that the Hide skill does not have the option to "Try Again".
Now, I can see this going both ways at this point. First off, I do not believe you can fail at a Hide check. A roll of a 1 still means you have successfully hidden, just not very well. If I roll a 1 on my Hide check, how does this mean I failed? If someone comes around the corner and tries to spot me, and gets lower than a 1 on their Spot check (because of low Wis or whatever), than I didn't fail, did I? So I stand firm in the belief that you can never really "fail" on a Hide check.
Now what makes you "fail" is the result of the opponent's Spot check. If there is nobody around to observe you (oppose your Hide check), you have no way of failing, because you don't have a target DC to beat.
Now, on the other hand, since there is no mention that you can "Try Again" on a Hide check (like there is with several other skills), that might conclude that you can't Take 20. Because, after all, Taking 20 is doing it over and over again until you get it right. But apparently you can't do it over and over again (re: Try Again) with Hide.
So I'd accept that:
(a) You can Take 10 with Hide.
(b) You can not Take 20 with Hide.
(c) If you have the time to spare, you can take extra time to Hide "better" thus gaining a circumstance bonus to Hide.