I would use the two that Arioch used in his examples.
So you would use the category bonus in lieu of a specific skill then? Did you mean you don't use stat checks but skills instead?
For remembering a detail, would you use mnemonics? And if a character did not have any ranks in mnemonics, would it be a roll at -15?
There is no question that players often want their characters to perform tasks that they have not developed skills in - I don't really see that as a problem. Not all characters can do everything well, even less so at low level.
I alluded above that there are a few ways of dealing with the issue (other than allowing a stat check, or allowing a 'category' roll as detailed by Arioch, as already discussed in this thread):
One widely (though not by me) used option is to reduce the number of skills so that a number of skills can be reduced to one. The 'advantage' is that players get 'caught short' less often as they don't have to be as judicious with their DPs.
Another is to tell players to get ranks in as many skills as possible ("if you spend all of your DPs on weapon skills, don't complain when your character is one dimensional")
My list of possible skills is huge (as many as I can think of without duplication), but as many skills do not incur a -15 penalty for not having developed ranks it becomes a list of things a character
can do (to some extent), and
can develop if they so wish. The result is that stat rolls tend to not be required, and as characters gain levels there is great scope for diversity and specialisation.
In the main, I think the problem is knowing which skill is the appropriate one for any given task. The more creative the players, the more likely an unusual task will crop up. I use the method of letting players first nominate what they want to do, and then nominate which skill they might like to use to achieve it (and to justify this choice). If I don't think the nominated skill is appropriate I will suggest an alternative (players sometimes suggest the skill in which they have the highest bonus, rather than the one most appropriate). Often it is just a case of breaking down the 'grand plan' into it's component parts - there is no skill called "bring down the evil empire" (well, apart from Battleaxe OB!).