The fact that I didn't write anything here yesterday, the day that Super Smash Bros. Brawl was released, is not a coincidence. That game is horribly addicting, just like its predecessor. My brother and I occasionally challenged each other in Super Smash Bros. Melee all the way from its release until a week ago, and we enjoyed every minute of it. It is a game that kept on entertaining even long after we have explored every single-player game mode and fought hundreds and hundreds of matches in its multiplayer mode.
Part of the reason I enjoyed Super Smash Bros. Melee so much over the last six years is because it is a game with incredibly easy controls. Every character has a limited number of normal attacks which are controlled only by combining the A button with directions on the control pad, a list of 4 special moves controlled with the B button, a few throws, dodges, and a single defensive stance that can be used against every kind of attack. It is very easy to learn how to play the game because of the simplicity, and because every character is controlled using the exact same inputs, it is very easy to fully understand multiple characters. No matter how long it has been since I last played the game, I can still remember all of the controls and all of my favorite moves with each of my favorite characters.
As a comparison, I want to mention another fighting game series that I like quite a bit: the Soul Calibur series. I like this series, own both Soul Calibur 2 and 3, and spent quite a bit of time and money playing Soul Calibur in the arcade, but I never played this series anywhere near as much as I played Super Smash Bros. Melee. In part, I think this is because of the difficulty of this series' controls. Every character has a long and elaborate movelist of dozens of completely unique moves, each of which has its own button input (which makes learning new characters the same thing as relearning all of the controls for the game), sometimes involving complex chains of difficult timing and/or tricky sequences like slide input. As such, I can never seem to remember even the basics of a character's moveset for very long. I need to refresh my memory with a half-hour long trip to the training mode practically every time I go to play the single-player mode, I need to occasionally check movelists in the middle of battle, and I can never remember a thing about a character's moveset after putting the game down longer than a few weeks. This makes coming back to the game somewhat intimidating, which has resulted in me not playing Soul Calibur 3 ever since I first stopped shortly after the game was originally released years ago, even though I left it incomplete and like the series quite a bit.
Another game I could compare Melee to is the Tekken series. I rented a Tekken game only once, and pretty much gave up on playing it within a day, after getting stuck, unable to continue, in a few characters' training modes. I think another major fighting game series, the Dead or Alive series, is a lot of fun, but much like with the Soul Calibur games, I can't seem to ever get back to playing Dead or Alive games once I have stopped playing for more than a week.
One series I can keep playing somewhat consistently is the Guilty Gear series, even though its level of general complexity because of various subsystems is fairly high. The game has all kinds of gauges and unusual rules you need to remember (including really unusual things like the Guard Meter, the limitation on combos, and the penalty you receive for not being aggressive enough), but the controls are not terribly complex. Every character has an analogous set of attacks based on the main attacking buttons, so all you need to remember for the various characters are the special moves and their inputs, which mostly are derived from a very limited set of possible inputs and follow certain learnable patterns. While it is not as quick as with Super Smash Bros, I can get back into playing Guilty Gear well within a very short time, so I return to the series fairly often (keeping with it is a different story, since playing it too much gives my thumb blisters).
Overall, I think a good fighting game should emulate the classic series, like the Street Fighter series, and keep things relatively simple to control. There should be as much similarity in control inputs between characters as possible, and these should be kept relatively simple. Requiring many complex button inputs for a character to even be decently viable just results in a game that is only appreciated by a very dedicated fanbase of very limited size, because it excludes too many gamers like me who like the genre, but are not so big of fans that we are willing to dedicate huge amounts of time and effort to play.