This is a tough question to answer, as it depends on the definition of the word "band". Did they have to have toured? Did they have to record an album? Did they have to have more than one actual member? Is the front man considered a member of his backup band, i.e. is James Brown a J.B. or Bruce Springsteen in the E Street Band? Etc. etc. etc. That having been said, let's give it a shot.
Les Claypool is definitely up there, as the front man of seven bands:
- Les Claypool and the Holy Mackarel
- Colonel Les Claypool's Fearless Flying Frog Brigade
- Colonel Claypool's Bucket of Bernie Brains
- Electric Apricot
He also has a solo album or two among his discography, usual featuring himself playing a number of instruments and some guest appearances for a track or two by various musicians.
Another musician who has been in a lot of bands is Bill Laswell. Looking through his discography, it's tough tell how many of the groups and bands he has been in would actually qualify as a "band", and how many of those "bands" he has actually led.
Bootsy Collins has also led a number of bands. In addition to being an important member of the J.B.'s, Parliament, Funkadelic, and Praxis, he has led the following bands:
- The Pacemakers
- The House Guests
- Bootsy's Rubber Band
- Sweat Band
- Bootsy's New Rubber Band (if you count that separately from Bootsy's Rubber Band)
- Science Faxtion
As for Dave Grohl, he has been in a large number of bands as well, and it seems he has led or co-led most of the bands and projects he has been involved with since the dissolution of Nirvana. These include:
- Foo Fighters
- Late! (recorded before Nirvana, released afterward; he was the only member)
- Harlingtox A.D. (recorded before Nirvana, released afterward; I'm unsure if he was actually the leader/front man or not)
- Probot (he was the only member)
- Them Crooked Vultures (co-leader)
He has also drummed with Queens of the Stage Age and Tenacious D since Nirvana ended.
Another musician who is up there is Sammy Hagar, who has been in a number of bands, and as the lead singer has been the front man of pretty much all of them.
- The Waboritas (his long-time backup band)
- Hagar Schon Aaronson Shrieve
- Van Halen
- The Hagar/Hart Project
- The Circle
We also have Robert Plant, who has fronted five bands
- Band Of Joy
- Led Zeppelin
- The Honeydrippers
- Page And Plant
- Strange Sensation (his backup band)
As @papakias mentioned in his answer, Steven Wilson of Porcupine Tree has also fronted a number of bands.
There's also the little known musician Paul McCartney, who has fronted
- The Quarrymen
- The Beatles
- The Fireman
- A variety of touring bands, whose names I've been unable to find
You also have George Clinton, who has been leading bands/groups/collectives since the 1950s.
- The Parliaments
- P-Funk All Stars
- A variety of one-off, studio-only groups, like Incorporated Thang Band, Our Gang Funky, and the P-Funk Guitar Army, among others.
Those are the only prolific frontmen I've been able to think of for the time being; I'll add more if think of anyone else.