If the player character is the body, the player him/herself is the soul.
It's a concept I'm trying to implement in my next few games because on the one hand, it's hard to keep a specific interested group for long-term campaigns, and on the other, player motivation takes a hit when characters do not continue and chargen must start again from scratch. Inspiration: Michael Moorcock's Eternal Champion series. Moorcock has linked his multiverse of books with the idea that each of his heroes (Elric, Corum, Jerry Cornelius and lots more) are all facets of the same character. They might share certain character traits, and certainly a similar heroic destiny, but they aren't aware of the connection. In fact, the link is usually pretty tenuous. I'd say the only reason the characters have the same "soul" (incarnated differently in different worlds) is that they're written by the same author. Elric and Jerry Cornelius, for example, only share similar fates, relationships and speech patterns (if they do at all) because Moorcock writes both and he has themes he likes to explore, writer's tics, his own particular cadence and obsessions.
Role-players are writers too, even if they are only in control of a particular character's fate. Though some players like to create different personalities and play them to the hilt, more often they use the same "voice" for each of their characters. Like a novelist, they'll have their own obsessions, interests and habits which will inform each character. Some will always want lots of options (wizards), while others prefer a straightforward profession like the fighter. Some can't help but joke around no matter the character's archetype. Some use inventive strategies, and others are never inspired to do more than "shoot". Some like to create character moments, and others like match-crunching combat. And those are players' traits, not characters, yet they trickle down to the character in some way. It's why talking about a player's profile is relevant.
Let's embrace that. Each character is an incarnation of their player's "soul". Now, what does that mean for our games?
The Continuing Story... It creates at the very least the illusion that the player is running a continuing character even if the campaign world has changed. You might want to transfer XP across dimensions to make this illusion more tangible. A player that reaches 5th level in one campaign could start at 5th level in the next. for example. This would work particularly well when there is no change of system (GURPS, Savage Worlds, etc.), but with work, could also be achieved across systems.
Recurring Themes... Just like the players, the GM is also a "writer" and has his or her own obsessions, tics, voice, etc. In other words, similar NPCs will tend to crop up, as will triggers for actions and narrative structures. Again, embrace it. If you always have an NPC who's goal is to humiliate a PC, try to make it the same PC each game. If you made an artifact the big MacGuffin for one campaign, introduce a similar artifact on the next one. Similarities will give texture to the Eternal Champions concept, while differences might create more surprise than they usually would. What is a character's true destiny? Sometimes the game will allow him to fulfill it, and others to subvert it. Players don't necessarily know which is which?
Wyrd... Players might be encouraged to take an Advantage/Disadvantage that makes them fated to do (or suffer) something. This Ad/Disad would stick to the player rather than the character and thus cross over to each campaign (though you could buy it off if you really wanted to - in effect retiring the Eternal Champion's soul and creating another). This Destiny or Wyrd could make a Champion always be fated to fall in love with an enemy, or land the killing blow to the campaign's Big Bad, or sacrifice herself in the climax. Destinies could be chosen after the first campaign and reflect something that actually happened, or could be known from the start. They could even be a complete mystery that only the GM knows (though soothsayers might reveal it).
But Don't Overdo It... You don't want to pull a Star Wars Episode One where everything feels like a rip-off of A New Hope. If all the beats are the same, there's little reason to play. The characters are certainly fated to become heroes, and to all know each other. The writers' voices will also create similarities between campaigns. So you may only need a small nudge from one of the ideas above. Try it out and let me know.
I think it's what I'm doing with my upcoming Savage Worlds campaigns and one-shots...