It is like circuitry so it is very important if you are going for a distictive sound.
If you where to hi pass a sound first with a steep curve at 100hz then was to add a guitar amp emulation to it after with a certain setting you would end up getting frequencies emitting below 100hz.
The basic example is, use a long reverb or a delay first, then do a heavy compression after that. You'll hear how the delay want's to fade away but the compressor keeps squishing the sound to the surface, until it fades under the treshold and suddenly goes quiet.
So yes. it's very important.
---------- Post added at 21:10 ---------- Previous post was at 21:07 ----------
And oh, even in menial tasks like EQing and compressing it does matter.
For example you compress a break to bring quiet hits up a bit. Then you think that the kick has too much BOOM in it and add an EQ after the compressor. This way you can cut the compressed signal out of it's bottom and if the boom was very heavy, the compressor will still be set off by the kick but you cant hear it since the boom is cut after the comp. Then again if you first cut off the boom (EQ before comp), the compressor wont react to the boom since it's not there when the signal comes into it - you've already cut it off before that.