I come back to this thread and find a versions poll. Might as well throw in my tuppence:
Jaguar - This version is practically a beta in final. It's obviously very different to the other versions of the game, and some features that were clearly always intended are missing. The developers probably realised part way through development that the Jaguar was going to be a flop and just wanted to get the game out there, so it's unfair to judge it like that. Thankfully, it made for one of the best Jaguar games, and this version is interesting because of all the differences, especially map and music wise.
PC - To me, the PC version has always felt oddly unrefined. Be it the strange additional voice acting, the frustrating new Electoon/1-up placements or the music only existing in medley form. It does make up for it's increased difficulty by upping the continues to 10. It's kind of a shame that Ubisoft keep using this version as a code base for more recent ports , but I can understand why starting with PC code is easier

. The PC version is made far more interesting by it's expansion packs, most notably Rayman Designer, which makes Rayman on the PC a lot of fun.
PlayStation - I'll try to be unbiased, as this was my first version, but I think even with the nostalgia aside, it's the best. It's one of the few versions where you get the full CD soundtrack, and on top of that a load of neat touches such as additional incidental drum loops on appropriate levels, fog effects for deep forest levels etc. For me, this is the definitive version of Rayman and the one that helped the Rayman series become popular in this country.
Saturn - Despite how much I've hyped up the PSX version, I'd like to go on to say that this version is pretty much on par with it, and this is coming from someone who only got a Saturn in recent years. While it's missing some of the features from the PS1 incarnation (such as the PSF jingles), in a typical Ubisoft fashion it adds some more (perhaps most notably the bizarrely cute little transition animations between maps). You also get all the good stuff - original Electoon placement, differentiation between the two Mozzies, CD soundtrack (arguably sounding even nicer on the Saturn) etc. I strongly persuade anyone who has never played Rayman 1 before to start on either the PlayStation or the Saturn.
Game Boy Colour - I personally don't think this belongs on the list as it is an entirely different game based on the same mechanics. With it's abundance of forest levels, lack of Rayman cast (Magician, Betilla etc.), tiny fairy collectables and Eric Chevalier soundtrack, it feels like how Rayman 1 would have happened in the Rayman 2 universe
Game Boy Advance - Interestingly, as of today, this is the only version of the game I have actually seen to the end. This is by no means the best version out there with it's muted colours (namely done so as to make the game visible on the original GBA's dim screen) and occasionally glitchy behaviour, but it is a good version to play if your on the run (unless you have the PlayStation version via PSP, of course). While based on the PC version, there are some changes made to make the game fairer on the small GB screen (perhaps most notably on the infamous Space Mama's Crater stage), which (asides from the Electoon placement) probably makes it one of the easier versions of Rayman out there. While the music is naturally a little tinny and simplified to work on the GBA, the composer has done a good job in converting the tracks, and there are a couple of neat exclusives too (I sometimes wonder if these are based on cut tracks from the original game)
DSI - I can't say a lot about this as it's the only version of Rayman 1 I've never played, but it is interesting to see that even today Ubisoft are keen on making strange changes between versions (see - the black music bars in Band Land). The addition of giving Rayman a crazy amount of health allows it to work as something of a training ROM, and I can imagine people wanting to complete this version of the game first so as to master the game before playing others (also known as higher skill levels of difficulty

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Wow, this is the first time I've been on the forum in ages and I start with this Epic Megapost. I'll have to be a bit less wordy next time
