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Pressing Tab completes commands in command-line mode, and its very smart. (Be sure to :set wildmenu to see a list of all matching commands as well.)

Even without wildmenu option, repeatedly pressing TAB key will cycle through the list of matches.

What's more, you can press <ctrl-D> to view the whole list of possible completions at one time. For example, enter ':colo ' then press <ctrl-D> and you'll see a list of all the colorscheme names. (The space in ':colo ' is important, since if you press ctl-D with just ':colo' Vim will just show you the 'colorscheme' completion. . . )

You can press the tab key in Vim to get command auto completion.

For example, :colo<tab> completes to :colorscheme.

Command-line mode has tab completion. I'm not aware of there being auto completion in the other modes.