Vi and its successor vim are both very mighty and well known tools. Some love them, some hate them. But overall, they're complex. If you are about to learn vim, it's probably a good idea to have a well arranged cheat sheet or reference card of the most important keyboard commands. It's not very difficult to find one, there are hundreds of thousands of cheat sheets, but many consist of HTML tables and are ugly or confusing. Only a few are really suitable for printing and having them on the desk. I know, all Emacs users and link list haters out there would kill me now, but I've collected a few of them for you. Note that you may use vi cheat sheets also for vim.
Note: Neither do I claim the copyright on any of these cheat sheets nor do I know the licenses under which they are published. You have to check that by your own. I've chosen only those which I think a free to download and print for personal use.
Simple vi cheat sheet
This vi cheat sheet is taken from the cheat sheet collection on digilife.be and consists of one page listing all very basic commands clearly. It's a good reference card to begin with.
Detailed vim cheat sheet
This two pages long vim reference card is also taken from digilife.be. It contains even more commands, but lacks a bit of the clearness the first one has. Use this if you already know many commands and just need to look up some more special ones from time to time.
Basic vim cheat sheet
This vim cheat sheet is not the most beautiful one I've ever seen, but it lists all basic commands clearly separated by groups. Also a good one to start with.
Very basic grandpa vi cheat sheet
This one is pretty old. But created in February 1995, it's still a very usable vi cheat sheet, also suitable for basic vim usage. I found this on public servers of the University of Idaho within the section of Robert Rinker. Thanks for that, Mr. Rinker!
Nifty vi cheat sheet published on Smashing Magazine
This one is designed by GoSquared and published on Smashing Magazine. Smashing Magazine is a famous blog about webdesign and normally they don't publish articles on such technical topics, but, er, why not? This vi cheat sheet is very basic but an eye candy, at least for those who like glossy effects. Good to begin with, but nothing for more advanced vim users.
Vim tutorial and keymap
ViEmu, the manufacturer of a vim emulator for Visual Studio, has chosen a slightly different approach. They provide several vim cheat sheets divided into lessons. They also don't list commands by category but in form of an English keyboard map. Interesting and definitely worth a look.
Detailed graphical cheat sheet of the basic commands
This cheat sheet has a little different approach, too. Instead of using lists or keymaps it shows graphically what the keys do and what their companions are. (Added Dec 4th 2012, from suggestion in the comments)
And #7 – build your own
Last but not least: the cheat sheet technique. This article on gentoo.org shows how to make your own personal cheat sheet. If you are not satisfied with all the others why not simply write your own?
That's it, hope you found some appropriate cheat sheet for you.