Where can you play Magic The Gathering online for free

3 places, 3 programs, all free and downloadable.

MTG Apprentice. Worlds most Basic MTG online program.
There is a program to edit the card library to start your own TCG or add cards.

Magic Workstation
There are a number of forums that use MWS to run tournaments, official and casual. The free version does contain banner ads and there is a 5 second wait before the application starts. But you can play free online and all the sets are downloadable and usable. It is alos compatible with a number of other TCG's.

Lackey CCG
You can make your own card games with images and setup program download updates for your game.
The program can even download MTG for free and several other favorite card games such as Pokemon, Star Wars, Wheel of Time, Megaman, Duel Masters, and many more.
You can also download Magic Online for free at the Wizard's of the Coast official website (wizards.com). But you will only be able to play with pre-constructed deck unless you buy online cards (which cost real money).

Once you purchase an account ($10), you are able to play with whatever cards you own for free as long as you like. You can at any time purchase more cards to play with, but you are never charged a fee for playing.