It's a fairly colloquial expression, and to a native speaker, it immediately suggests:

"Be frank, don't be afraid to tell the truth has you perceive it, even if you're afraid we won't like what you say" --- in other words, tell us what you REALLY think...!

It doesn't mean 'be as honest as you are capable of being'

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Note added at 27 mins (2005-08-17 12:27:48 GMT)
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To Koray:

It\'s terribly difficult to explain the nuance of meaning here, but trust me, there IS one!

\"Be as honest as possible\" suggests pushing telling the truth, like saying to someone \"How many cigarettes have you smoked today?\" C\'mon, now own up, tell the truth.\"

But \"be as honest as you like\" means be frank, don\'t pull punches; you WOUDLN\'T say \"How many cigarettes have you smoked today, --- now, c\'mon, be as honest as you like\" --- that would be silly (unless you meant it ironically); but you might well say \"What do you think of my new dress? --- now c\'mon, you can be frank with me, be as honest as you like\"

It\'s all a matter of subtle nuances, and the different expectations of answer between asker and answerer --- a question of \'feeling\'; and such factors hold good EVEN for \'a simple questionnaire\' --- particularly if it is a company trying to get frank feedback from its employees, for example...