Much like the Avengers, the X-Men can be adapted to a Star Wars setting—though, in my eyes, it is a much more difficult adaptation. The idea of being a 'mutant' as the unifying factor of the group just simply doesn't work in the Star Wars galaxy. My initial thought was to have 'mutation' turn to 'Force use' as the reason for being persecuted, but this simply doesn't work for much of the team. Therefore, the angle I am taking is more along the lines that professor X is assembling unique individuals to help overthrow the Empire. THIS is their unifying goal. Some are Force users, others are aliens—both of which are oppressed under the Empire. Thus, it works for the most part. Those who don't fit into those categories are a bit more difficult to adapt, but can be explained away as sympathetic to the cause—wanting to overthrow the tyranny of the Empire.
X-Men in the Star Wars Universe:
Charles Xavier was a young Jedi Knight in the closing stages of the Clone Wars. Along with his close friend and fellow knight, Magnus, Xavier survived the purge. The two of them resolved to overthrow the Emperor, but soon had a falling out when Magnus felt Xavier's methods were too 'tame' and not direct enough. Their final 'disagreement' left Xavier paralyzed from the waist down. Undaunted, he continued his quest, using his powers to hide himself from the galaxy at large, to build up enough money to buy a remote facility and set up as a seemingly innocuous boarding school. There, he would find and train individuals of all kinds to help in his fight against the Empire.
Game-wise, Xavier would have to have some rare kind of nerve damage (or perhaps an allergy?) that prevents the use of cybernetics from simply 'fixing' his broken body. His powers can all easily be explained away through the Force (telepathy, telekinesis, etc.).
One of the more difficult people to 'translate' into Star Wars, this version of Cyclops would not be a mutant, but rather a boy (the son of an old republic war hero), who was injured in a crash that (supposedly) killed his parents. He was subsequently taken in by Xavier, who was actually an old family friend of Scott's (Cyclops' real name) father.
Scott's vision was damaged in the accident, resulting in the cybernetic replacement of his eyes. In learning to use these 'new eyes', Scott became incredibly perceptive–literally the eyes and ears of Xavier. Later, one of Scott's team-mates (the "Beast") devised for him a high-tech visor that improves his already incredible perception. Scott's steady nature and dedication to training also make him the de-facto leader of the team.
Stat-wise, Scott is just a normal guy. He has no 'optical blasts', but instead is a remarkable marksman and scout, using his visor and his cybernetic eyes to identify dangers to the team.
Bobby Drake is a young man with natural force abilities, which professor Xavier is working on building. But most exceptional is his Cryokinesis—a rare power that even Xavier does not possess.
Stat-wise, Ice-man is just a young man. He doesn't cover himself with ice, or 'fly' with ice bridges or anything like that. He just has the power to freeze things and is learning other 'tricks' with this power.
Archangel is simply a winged humanoid alien. He has the natural ability of flight and the desire to overthrow the oppressive Imperial regime.
A strong and agile, fur-covered humanoid. But despite his bestial appearance, the "Beast" is actually an incredibly intelligent scientist—one responsible for developing much of the team's gadgetry. Stat-Wise, he would likely have a 4D Strength and Agility, and close to a 5D Intelligence.
Jean Grey is a powerful young Force User, very much like Professor Xavier, himself—only with a more troubled soul. She constantly faces her darker-side when utilizing her power.
These would be the "Core" X-Men, but others could be added. Those who seem to work best (for me) include:
Nightcrawler: An Alien capable of amazing athletic feats (and of clinging to sheer surfaces). His amazing agility and mobility seem to make his movements seem 'almost' like teleporting, but no, he would not have that power.
Wolverine: An escaped and amnesiac Imperial super-soldier experiment. He would have to be toned down quite a bit from the books—his healing factor being a bit slower and unable to bring him back from death.
Storm: A Force User attuned to the natural elements of wind and water—able to 'summon' storms and the like through a special 'weather manipulation' force power.
Colossus: Re-imagined as a cyborg—though without the metal skin, but rather a suit of armor he wears in addition to his strength-enhancing implants. These implants were given to him by a crimelord (involuntarily) for whom Colossus was forced to work until escaping to join the X-Men.
Banshee: Hated the fact that a male character was given the name of a 'female' monster. So, lets make this Banshee a female near-human and force user with amazing vocal abilities—which can be enhanced by her force powers to produce sonic-shockwaves or even to enhance her 'affect mind' powers while singing.
Shadowcat: Alas, the cool 'walking through walls' power is just too much for me in a Star Wars setting. Rather, I would re-imagine her as a very young, but very capable thief, capable of getting through ANY kind of security device or even computer firewall. Perhaps she does have latent Force powers that Xavier is trying to develop in her.
Lockheed: The dragonlike mascot of the team.
Psylocke: A woman with a shady past. She'd have Force powers, enabling her to fight very well with her katanas and mentally manipulate people. But no 'psychic knives' or anything like that. She'd also be very morally questionable, in danger of going over to the dark side.
Forge: A technological savant with cybernetic prosthetics. A mentor for Beast.
Gambit: A gambler with a shady past. Latent force abilities give him remarkable precognition and even minor telepathy (thus making him a good gambler). They would also allow him to use a staff very much like a lightsaber (enhanced attack and defense). He would also be a master of thrown weapons.
Cannonball: A natural pilot with latent force abilities.
Some X-Men, however, just don't work. Either due to their powers being too 'out there' or the fact that I just think they're stupid (very scientific, I know). These include:
Sunfire (Never liked him much, but I suppose you could just turn him into a pyrokinetic)
Thunderbird (Never liked him much, either)
Rogue (Power just doesn't fit, and a lot of her 'hook' goes away if she doesn't have it)
Longshot (Power just doesn't fit. He just has 'good luck'? Plus? He had a mullet)
Dazzler (She generates pretty lights when she sings... disco songs. Silly)
Jubilee (As much as I LOVE jubilee (and I actually do), I can't reconcile her powers (again, more pretty lights) with any thing Star Warsy.
Bishop (Never liked him much.)
Marrow (Never liked her much. Hate the idea of ripping bones from your body and throwing them at people).
Maggott (Too stupid for words. Seriously, who thought this was a good idea?)
Cable (Never liked him much. Backstory is WAY too convoluted).