Official on Suspend:
* The initial suspend, like morph, is one of those abilities your opponent can't get around. Suspending is not the same as playing the card. It neither uses the stack nor allows a response, which means there's no practical way to counter it. For those who require more technical detail: your ability to pull your own card out of the game is static, not triggered or activated.
* Once the card is suspended, everything else that happens with it happens on the stack. Like everything else that says "at the beginning of your upkeep", the removal of a time counter gives people a chance to respond. (Someone, for example, could Stifle the removal of such a counter, delaying the spell another turn. You know, if that's what floats their boat.)
* When you take the last counter off, it's time to play the spell. For nothing. Woo-hoo! Of course, this action still uses the stack. Now the spell can attract a Counterspell.
Source:
http://wizards.com/default.asp?x=mtgcom/daily/aa245 ("RULES-IN-A-BOX")
Full technical rules for suspend:
http://wizards.com/default.asp?x=mtgcom/daily/mr245 (scroll down)