Update - 12/14/2022
The popular tournament bracket site, Challonge.com, began supporting games with more than two participants per round. You can set the tournament format to "Free for all" and specify the number of maximum players per round. It will automatically try to distribute players as evenly as it can. You can decide how many players advance in each match. Those players will advance to the next round where they would be distributed evenly again.
I have found that creating tournaments with a four player free for all scenario can require a fair balance of intuition and logic. You have to ask questions such as whether or not three player matches would work and how many winners do you want to move on from one round to the next.
Minimum Group Sizes
What group sizes are acceptable for the game you are running? Will you allow groups of three or two? The more strict this is, the more byes you will have. If you had 15 players, you could have three groups of four and one group of three. However if you did not want to have a three player group, you would need to turn that group of three into a group of two and have one bye. I believe groups of three are preferable to having byes. You may be concerned about players teaming up, but that is an issue you can encounter even in a four player FFA. There just has to be an honor system, and players who break the rule would be subject to the tournament operator's judgment.
I think the point where intuition comes in is that you may be ok with 3 player matches, but you maybe don't want the final match to be a 3 player round. So you may want to rearrange the semi-finals to ensure that the final round is between two players. Alternatively, you could do round robin style 1v1 matches between the final three players. What you decide to do here may depend on the game you are playing and the group of people you are playing with.
It is difficult to create something that algorithmically resolves a list of players into four player FFA bracket without any flaws. However, I was able to create a program that sorts players out into the biggest possible groups. I added multiple options so that you can tweak it to find what works for you in your situation.
You can download the stand-alone program here:
-----This requires Microsoft .Net Framework 4.0
You can view the source code here:
Smash Bros Victory Conditions in 4 Player FFA
One more side note in regards to smash bros specifically, if you decide to have two winners from a four player round, you could simply take the first and second place players or you could award victory to the last surviving player and the player with the most kills. The latter method is how the official Nintendo tournament was run at E3 in 2014.