There is still some confusion on the actual, official, release date of the Spore Creature Creator, but if you want the full version now, it's available on Direct2Drive's UK site, right here - and you can purchase it right now - at least if you are in the Europe. It's 4.95 GBP for four times as many parts for building your own dirty creations - and you can get it for free if you go and preorder the full game.
The official site has not been updated yet with download or purchase links, so the only obvious source for the trial version is still to scour for it from any number of torrent sites - and we recommend you exercise caution when dealing with non-official download sources.
Update: It looks like June 17 is holding true - the editor (free trial) is now available on the European EA sites - like here on the EA UK site.
Spore Creature Creator Date Confusion