Audition, a multiplayer dancing game by Nexon (developers of games such as Maplestory, Combat Arms, etc), which is also totally free.
You start out by creating an account HERE. If you already play a game by Nexon, you should use that account. You then create your own character, which you use throughout the entire game. (WARNING: The character creator will automatically pick the gender you chose for your Nexon account, so if you want to pretend to be a shy little girl and pick up cute boys, pick female at account creation!)
At start you won't have any fun clothes, faces or haircuts to pick, but later on you will earn something called 'Beats' which you can buy a nice amount of clothes/haircuts with at the mall. The other choice is to buy credits from Nexon with hard cash, to get the nicer clothes faster.
Now moving on to modes. It's recommended to start with the tutorial, but the tutorial only shows you a small part of the game; the "Normal" mode. Read below for a short description and screenshots/videos on some of the different modes.
Normal (Normal Practice, Normal Individual, Normal Teams, Choreography):
This mode is played by typing in the correct combination of arrow keys as fast as possible, while keeping beat with the space button.
Normal Team gameplay:
Moving on to Beat Up (Beat Up 6-key, Beat Up 4-key):
This mode is played by pressing the numkeys (741 = Left, 963 = Right) when the arrows are as near as possible, while still keeping the beat with the space button. From my experience, this is the funniest, most challenging mode. Tip: Listen for the melody you are creating as you're timing the arrows, and use that to track the notes easier.
Beat Up 6-key gameplay:
(PS: You can make your interface smaller by pressing minus, and you put it back by pressing +. This guy is playing with small interface, which can be a bit hard to get used to for new players. He is also playing one of the harder songs in the game, don't be intimidated!)
And this one for all you fanboys out there, this one is played by CheZDa:
There are several more modes once you move on from the beginner servers, which would be too many to list. But there are event-modes like Wedding, Story, etc.
There are also tournaments being hosted every day where you can win amounts of credits, and stuff like that.
As you level up, you will have to license, which you do in the 'Free Servers'. The first license is taken at lvl 5 (when you should normally have leveled up to 6, you will see a blue button saying "License" next to the "Make Room" button.) This first license is played in Normal.
A tip before you start: Don't settle on easy, slower songs. Challenge yourself and play songs slightly above your own capabilities. This way; you learn.