Some of the following aren't technically alternate Rimmers. Think of this more as a section dedicated to ice-skating mongooses.
Arlene Rimmer (Parallel Universe)
We meet Arlene in an alternate reality where gender roles are reversed. As the name might suggest, Arlene is the female version of Rimmer, complete with her own chat up lines: "Why? How many have you got?"
Peace-loving Rimmer (Polymorph)
We meet this version of Rimmer after his anger has been sucked out of him by the polymorph (cunningly disguised as his mother). This new Rimmer seems to think that all of the world's problems will be solved by leaflet campaigns.
Ace Rimmer (Dimension Jump, Emohawk II, Stoke me a Clipper)
What a guy! Ace's first appearance is in Dimension Jump - he is a traveller from a parallel universe. He has all of the charm, charisma and sexual magnetism that, well, quite frankly, our Rimmer lacks. We meet him again briefly in Series VII and VIII.
Smart Rimmer (Holoship)
He appears briefly after Kryten performs a mind patch on him, in the hope that he will become smart enough to pass the holoship exam. It works, for a while, and we are treated to a brainy (and snorting) Rimmer.
Insane Rimmer (Quarantine)
This section wouldn't be complete without giving this one a mention.
After contracting a holo-virus from the crazy Dr. Lanstrom, Rimmer becomes
Clad in a gingham dress and pigtails, Rimmer is joined by his sidekick, Mr. Flibble. Together, they answer to the King of the Potato People.
Angelic Rimmer (Demons & Angels)
Angelic Rimmer appears when the crew visits the 'higher" version of Red Dwarf. A ship that is not held back by the natural balance of negativity.
Demonic Rimmer (Demons & Angels)
Clad in stockings and suspenders and more piercings than a very pierced person, Demonic Rimmer's home is the "low" version of Red Dwarf.
William (Billy) Doyle (Back to Reality)
Billy Doyle is the guy who is "playing" Rimmer in the virtual video game, Red Dwarf. His favourite cologne is 'Odour Yak Urine'.