This is the favorite of all since apart of sending the process into the background you don't have to worry about the text output dirtying your terminal:
nohup command &
This not only runs the process in background, also generates a log (called nohup.out in the current directory, if that's not possible, your home directory) and if you close/logout the current shell the process is not killed by preventing the child proccess from recieving the parent signals when killed (ie. logging out, by SIGHUP to the parent, or closing the current shell).
There's other called disown but that's rather a extension of other answers rather that a method in itself:
command & # our program is in background
disown # now it detached itself of the shell, you can do whatever you want
These commands do not allows you to recover easily the process outputs unless you use a hackish way to get it done.