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I don't see anything in the rules to say one can't, but The Bard's Lore Master ability seems to imply that one otherwise couldn't:
At 5th level, the bard becomes a master of lore and can take 10 on any Knowledge skill check that he has ranks in.
Is there something in the Pathfinder rules that explicitly says one can't take 10 on Knowledge checks? If not, does the Bard's 5th level Lore Master ability actually do anything?
Nowhere in the Pathfinder Core Rulebook does it say that you can't take 10 on a knowledge check. By RAW, one can take 10 on any roll (except Use Magic Device), provided they are not under stress, in combat, in immediate danger, etc. - unless you have the explicit ability to do so.
The wording is, admittedly, a bit unclear for Lore Master, but that's actually what it's saying: even under stress, in danger, or in combat, a bard can take 10 on a knowledge check.
The requirement that you must be able to retry the check only applies to taking 20, because taking 20 implies that you will fail many times before succeeding (and that you incur the consequences of doing so). This rule, by the RAW, does not apply to taking 10.
However, what RAW says may not be a good idea in this case. I dug up this old thread on the issue at the Paizo forums, and they make some good points.
While RAW does not specifically state that you must be able to retry to take 10, most people seem to agree - and I've personally found - that this makes the most sense. By a very common houserule, I'd probably apply the rule for taking 20 to taking 10 - that is to say, you must be able to retry a check to take 10.
Because you cannot retry a knowledge check without more information or a new prompt, you cannot take 10, because there is the possibility you would fail the first time. Unless, of course, you're specifically granted permission to.
The are also some arguments for allowing to take 10 on Knowledge checks (also included in the same old thread).
For many cases "taking 10" will reveal only superficial knowledge, the characters with enough skill ranks and intelligence should have anyway. Of course, even a high-level wizard might, in the heat of battle, forget some monster's abilities, or won't be able to remember the king's second cousin's wife's name in an important conversation, but without stress easy (relative to character level) questions should be allowed for take 10. If a GM allows players to advance the story with simple low-DC Knowledge checks, it's his problem.
And bards are just able to remember some things when it's mostly convenient, perhaps a "Lore master" is just a wrong name for the ability. I'd imagine it closer to "total recall" (a'la The Mentalist) than to any kind of "lore".
