Many games allow you to create characters, but the good ones require you to systematically destroy them as well for the sake of balance.
The character creation process is a fun and an important part of how you play the game.
I remember a few games where I spent days creating characters and only hours actually playing the game. Still, I remember those games fondly.
In games I played which require character creation I usually had most fun in the first few parts (levels, regions) of the game. When I learn the basic gameplay mechanics, I see which ones I like and where I made mistakes - and then make a new character. And so a few times.
In most games, as I progress, my choices lessen and not widen. When choices become few, play becomes grind.
It is then when a character dies.
This holds true not only for role-playing games, but other games as well. For example, in strategy games, the strategy you employ is your character. When you're out of options, out of new things to try and strategize about: the archenemy of games, the master of oblivion - boredom - becomes triumphant.
A game does not end when I beat the game; it ends when I find out how to beat it.
Life is change, and to keep a game alive the possibility of change has to be present.
The most extreme solution is the one the card game Magic: the Gathering employs. To keep the game alive, they completely reinvent it every few months.
A less extreme, but not quite effective solution with computer games is addition of content and minor gameplay changes through patching. Games which rely solely on absorbable content get old fast.
The best solution is to involve the players. Balanced PvP or other competitive or non-competitive interaction among players can infuse a game with life. The golden rule is: simple rules, complex gameplay. Simple tools, many options.
Character creation is not a static act, but a dynamic process; it is the game itself.
In games which forget this, characters get more depressive as they age.
In games which understand this, characters are immortal.