Some characters seem to be one-offs that don't have much lasting power, while other characters seem to be playable ad infinitum. Consider, for a moment, the enduring charm of characters like Sherlock Holmes or Captain Kirk. This doc discusses things you can do to make a character playable over a long-term.
Character generation is perhaps the most important time in determining the long-term playability of a character.
Characters designed for point efficiency or maximum torque (i.e. min-maxing) tend not to have much play value over the long-term, if even the short-term. Conversely, a character concept that is so vivid and so compelling that you have to strain to limit the number of quirks is probably going to be much more playable for much longer.
This is not to say that you can't have a good character concept and design a character for point efficiency, but you should give priority to the former over the latter.
Perhaps the best aid you have in making a good character concept is a character history. If you have a so-so concept in mind, writing up a brief history for the character will help you flesh out their motivations and connect them with other characters in the gameworld.
For more insights on making a delightfully quirky character, see The Quintessence of Quirks.
A popular "game within a game" is for the players to try to figure out how to work (*cough* abuse *cough*) the rules in such a way that they can make an absolutely killer character right from the start; say, a wizard who can summon up demons from the abyss and take no fatigue at all.
To be sure, this is an interesting academic excersise, but it doesn't allow much room for growth. You can't see a character grow from a naive, wet-behind-the-ears farmboy into a dashing adventurer if he already starts out as Ulrik The Unbeatable.
This isn't a condemnation of power-gaming part and parcel, some high-concept, high-powered characters have a strong enough character concept to make them playable over a very long term, but leaving some room for growth can give your character some goals to reach and incite you earn his glory through play.
A good way to help your character be useful to the game master (and to the other players as well) is to build into him a number of traits that help him to start an adventure.
Perhaps one of the best 'Hook' characters we had in our Victorian campaign was Sir Percival Blakely. He was a well-to-do aristocrat who was in charge of the local police squad, was a compulsive gambler, and had a number of old rivals. It was a cinch for the GM to start an adventure with him because there was his stately mannor where the PCs could all meet up, any number of important NPCs would plausibly be hanging around his estate, curious treasures that he had aquired or won at the gambling table would show up, and police reports would come in for him on a regular basis. Percival Blakely was just the perfect Hook for nearly anything.
As mentioned earlier, a character history can be a big help in fleshing our the character concept, but it can also help you to be a good hook. With an explanation of the character's experiences and past relationships, it can give the gamemaster a lot of material to work with in using your character as an adventure hook.
The best kinds of advantages and disadvantages are ones that have a possible game-efect (either helpful or deleterious) but always have good humor value in real life. An Odious Personal Habit that is annoying to the GM / players as well as the PCs and NPCs is hurting you not only in the gameworld, it's hurting you at the table.
If a character makes people laugh, they'll want to see him again. Think of the recurring characters on sketch comedy shows that the audience always cheered for (Stuart on Mad TV, Wayne and Garth on SNL, Barry and Levonne on The State), and try to be one of those characters that the audience just loves to see.
After you've generated an interesting character, you have to keep him interesting.
Just like any good comedian, a good character doesn't re-hash the same gags over and over, he comes up with new jokes and antics. If you don't want your character to get boring and stale, you should come up with new lines for him to say and new actions to take.
The GM has to do planning before an adventure, and so should you. Take some time to think of new lines and gimmicks before the game begins. When the game is underway, play of other characters to make both them and you more humorous and interesting.
Over the course of play, a character might aquire new disadvantages and quriks, mostly via failed fright checks and health rolls. At the time, aquiring a new disadvantage can seem pretty devastating, but there's a silver lining: it keeps you interesting.
When a new disadvantage is aquired, you don't have to buy it off right away. Instead, consider buying off one of your older disadvantages, probably one that you got a character creation and one that is possibly getting a little stale. To complement your new disadvantage, you might even gain some new quirks (or recycle old ones) to help highlight this new development.
Side note: If you started with such a vibrant character concept that you were forced to pare down the disadvantages and quriks that you wanted to take to get under the cap, you should be excited to get a new Delusion or Quirk and have a Great Idea for what it should be.
Additionally, the GM might award you a new advantage or transform an existing one into a different one. In addition to being a good "candy" reward for players, it can help keep the characters interesting.
The other players in the gaming circle can be a big source of help in promoting a character's career. Specifically, the best way other characters can help is to form a unique relationship with the character. A pre-requisite for this is that the other players must like the character and want to see him succeed. (See Being a Team Player for advice on how to make the kind of character the team will enjoy.
On a GURPS character sheet, you will typically see a handful of quirks that help define the character's personality. These quirks typically are self-contained and make no ties to any other specific character in the party. To bind other characters more strongly to you (and to bind yourself to other characters), it is a good idea to write down a few quirks that define your relationship to other characters in the group. Examples include:
One of the best examples of two-peas-in-a-pod characters is Pinky and the Brain. Nearly all the quirks they had involved the two of them.
Brain: "Pinky, are you pondering what I'm pondering?"
Pinky: "I think so, Brain, but where are we going to find a pair of Rubber Pants that large?"
Brain: "Just wait until tomorrow night."
Pinky: "What are we going to do tomorrow night, Brain?"
Brain: "The same thing we do every night: Try and take over the world!"
This close interaction made the two little mice feed off each other and kept the viewers coming back for more. Finding just one other character in the group that you can link with can help boost the playability of your own character. Making a link with two or more of the other players in the team can help even more.
A GM that wants to encourage a tight-knit group might allow players one point per relationship quirk, in addition to the normal 5 individual quirks.
In creating a connection with another PC, keep in mind that it doesn't always have to be a "best of friends" type of arrangement. A little "rivalry" can be one of the most entertaining relationships that two characters can have. There are plenty examples of "oil-and-vinegar" types of relationships that were very entertaining: Oscar and Felix on "The Odd Couple", Hawkeye and Winchester on M*A*S*H, Spike and Buffy on BTVS, to name a few.
One point to remember along these lines: if you're going to create a character that is a rival with an existing PC, remember to keep it "friendly". Two teammates can exchange verbal jabs from time to time, but when push-comes-to-shove, they should fight side by side as best of friends. The principle of "loyal opposition" applies here: most of the time they're "opposed" to another character in some way, but at the end of the day, they're still loyal friends.
One note: If it becomes clear (to the GM or anyone else) that only one of the players seems to be enjoying the Friendly Rivalry, it's probably not good for the game.
Another note...particularly resourceful GMs can develop ways of tweaking with rivals, such as making them save one another's life, or play one another's characters (through some contrived "body swap" plot).
What The Game Master Can Do
The GM can play a big part in the long-term playability of a character.
Give Advice at Generation
If you're a game master with some experience and know what you like to see and don't like to see, pass on some of these kernels of wisdom to your players. When players are drafting up characters, give them feedback about how funny / interesting you think the character concept is and what might be done to improve it. Look for ways that the new character could connect to others in the group and offer some "Relationship Quirks" that would help tie him into the group. Think of ways that you could use the character as a hook for an adventure and possibly suggest changes that would make the character an even better hook. This last point will help you when you sit down to...
Make Character-Centric Adventures
Perhaps the best thing that a game master can do to keep a character vibrant and interesting is to design an adventure around him. This is easier to do for some characters than others; some flowers seem to bloom all by themselves, but other flowers will bloom when they're put in the sun. Try to give every character a chance to bloom, not just the self-blooming ones.
Ask for Ideas
Ask a player where he would like to see his own character go, but also ask a player where he would like to see somebody else's character go. This is similar to the strategy used to pick out a good birthday present for someone (don't ask them directly, ask one of their friends) and can be equally rewarding.