You should ask questions that need a person to answer, that you won't find just googling. For example, things specific to a particular area, or very time-specific (relevant here and now). A personal opinion or a very detailed query that maybe no-one has come up with before is another possibility.
I suspect I've been asked this question a lot is that Google has just taken over Aardvark, so it is in the news. So both journalists and curious new users are trying it out, not knowing what to ask, and so asking meta-questions. Aardvark themselves answer this question on their public FAQ but possibly they don't phrase it well enough to hit the top of the google results.
There is a good reason why I say don't answer questions you could google. Doing so would be a bit rude. The person answering the question will then google, find the answer and send it back to you - you've just made them do something you could have done yourself. If someone does this to you and you are frustrated, may I suggest www.lmgtfy.com - like this! It's a bit cheeky but in my opinion not too rude, and gets the message across in a gentle and humorous way.
I've found static web seaches don't work too well for time sensitive searches. For example "What is the highest mega-pixel digital camera?" or "What is the fastest computer?" relies on the page pointed to being updated. If you happen to hit an old article as top result you might not know the answer is out of date.
Aardvark is also good for opinions, but remember while checking out why you should listen to an opinion on the web is hard, checking the authority of an Aardvark answer is even harder!