I like to say that it's important to recognise and state your assumptions up front, because that is the basis of logical thought. If you aren't assuming anything, you aren't speaking logically or rationally. If you don't know what you're assuming, you don't know where your reasoning might fall down. The problem, however, is that it is sometimes very difficult to see what you are assuming when you are making an argument. It's not based on assumptions you consciously place on the table, label "Exhibit A", and refer to as conditional. Your assumptions are quite often subconscious, and you won't necessarily know what they are before you use them.
That doesn't make it less important, just less likely that you will know your assumptions until you go looking for them. You have to question what you believe to be true. When you analyse your own thoughts, you will find yourself at some level saying "Well, of course that's true. Everyone knows that.". That's an assumption, but it might not be the very base level you could get to. Keep digging, and you'll be surprised just how much you've been taking for granted.
Mokalus of Borg
PS - You will, however, assume you are correct in all your beliefs.
PPS - Despite knowing that, in general, you must be wrong about something.