I've been thinking a lot about this topic, what with HoXPoX going on and promising to change the franchise at it's core, as well as other threads that are going around right now with similar "change things up" as the premise, such as the Infinity Warps thread... and I'll be honest, certain members have a way of getting the creative juices flowing. Anyway, without further ado...

Reboot the X Men. Do you want to take them all back to the days of the original X Men? Before then? Do so. Do you want to do a soft reboot style kind of thing and maintain some kind of franchise history? You can! Do you want to even keep all of the primary history of the X Men and just further the concept of the franchise? Well, you can do that as well! The general idea here is that you can do anything, and what you do is entirely up to you.

Personally, I believe that there are certain aspects of the franchise that have gotten a bit... heavy. There is a lot.of baggage within the X Men and some people might argue that said baggage adds to the franchise, but I'm not sure that I agree. Similarly, there are a hell of a lot of characters in this franchise, the most of which don't get decent attention because of the sheer amount of them.

So: I would do a soft reboot. Take the X Men back to a simpler time when they were hated and feared and they hadn't gone through numerous extinction level events, where the main players of the franchise hadn't died and come back to life - sometimes multiple times. We'll say it's a few years into the history of the team, ~6 years or so following the formation of the original X Men. Speaking of, the general concept would be the same, but the original X Men would be Cyclops, Marvel Girl, Angel, Storm, and Thunderbird. Beast would be a colleague of Charles and Iceman would be younger.

The concept of the franchise would pick up from the original X Men, now in their early twenties, picking up from where a now deceased (for real, at least at the start) left off and heralding a new generation of X Men. They would be centered at Xavier's, with both a Blue and Gold side to the team as well as a team of New Mutants. Otherwise, there would be other offshoots of the X brand as usual, each focusing on their own concepts. The teams would look something like this:

Uncanny X Men
The BLUE team, co-led by Cyclops and Rogue. The blue team.is a rapid response squad, reacting as quickly as possible to threats made by and against mutantkind.

Cyclops
Rogue
Gambit
Psylocke
Colossus
Polaris
Archangel

Extraordinary X Men
The GOLD team. The gold team are the face of the X Men, going out and taking care of the big battles - practically the Avengers level stuff, but mostly still mutant related and advancing the X Men's cause.

Phoenix
Northstar
Storm
Thunderbird
Scarlet Witch
Bishop
Penance (Monet)

The New Mutants
The next generation of mutant heroes, and, well, the teen team. They are currently training to be the best heroes that they can be while also dealing with all of their interpersonal.and extrapersonal drama, while they all ask themselves: how hard is it to be heroes and also deal with trying to get through their adolescence?

Iceman
Mirage
Cannonball
Magma
Sunspot
Magik
Boom Boom

X-Factor
The government sanctioned strong right arm of mutantkind, X Factor works closely with both SHIELD and the X Men with the general mission statement of maintaining peace and order throughout the world. They're also just generally trying to make mutantkind's reputation better.

Banshee
Omega Sentinel
Quicksilver
Shadowcat
Wisdom
Sunpyre
Multiple Man

X-Force
X-Force is what you might imagine them to be: a team of well minded, like minded individuals who have been brought together to quietly take care of threats to mutantkind before they become an issue. They're unafraid to do what it is that must be done.

Wolverine
Kwannon
Cable
Mystique
Sunfire
Destiny
X-23

Exiles
A group of survivors from dead universes who no longer feel as though they have a place in the Multiverse. They've been chosen by the Powers That Be to travel between universes with the express intent of either saving them, or excusing them entirely.

Blink
Mimic
Revenant (Rachel Grey-Summers)
Morph
Nocturne
Sabertooth
Magneto

Certain characters would be modernized and racebend as necessary (eg. I'm envisioning Iceman as Asian and Magma as dark skinned) in order to make the franchise a bit more diverse. I was also thinking that there would be an X-Men Unlimited anthology series that would be a vehicle to tell stories that would have happened in the past that hadn't been seen, sort of in the nature of DC's Secret Origins series.