First, sound is perceived when things bump around in your ear, which is generally caused by air bumping around.  Moving your pick through the air therefore causes sound, and striking the strings is amplified by the guitar, creating even more sound.  Thus, pick sounds are unavoidable.

That said, there are various things you can do to lessen the sound.  One is your type of pick.  A harder, thicker pick will create more sound, so you could choose a thinner and/or softer one.  (As Lennart notes below, the opposite may be true for acoustic guitar.  It also depends how you play.  Picks are cheap, so get a few and experiment!)

You can also hold the pick more loosely, so that your fingers absorb some of the impact when the pick hits the strings.  Picking on an angle and drawing the pick across the strings will also create more pick sounds; the less the pick is in contact with the strings, the less sound it makes.

And of course, you can just play softer.  Don't hit the strings so hard :P.  On the other hand, the behavior you describe in the question comments is caused by striking too softly or not following through.  You want a smooth, continuous motion through the strings.  While it's impossible to avoid entirely, try to avoid the inconsistent motion caused by the strings impeding your strumming.  This just takes practice, and a strong wrist.