If you're loving the gameplay found in Minecraft and are looking to try out some similar games, give these games a try. Some are even free to play!
Not all of these are Minecraft clones, however. Infiniminer was actually a huge inspiration to Notch when he started building Minecraft. Also, Notch was part of the team that worked on Wurm Online before leaving to go do his own gig.
UPDATED 06/17/2013
Games Like Minecraft
Did I miss one? Tell me!