Something that one player and I always do is make his characters for my campaigns together. It's something that works really well, for both of us, and I think it's a practice that really helps flesh out a character and plant some solid story hooks.
He usually comes up with an idea or concept on his own, thinks about it a bit, and then comes over and we hammer out the details. As a DM, I can offer suggestions that he may not have thought of, or outright tell him if a power/feat choice is a bad idea (like focusing on an undead-hunting theme in an undead-light campaign).
One of the first things we discuss is if his character works in the campaign. For instance, he had an idea for our upcoming Dark Sun campaign to be a Raven-based warlock. Problem was, not only is this an arcane class (meaning that since it's Dark Sun, there should probably be a bit more history/backstory established as to how he is able to use arcane magic) but he also wanted to use a Spellscar, something from Forgotten Realms with FURTHER arcane magic connections.
If he had showed up on game night with this character, I would have been put in a tough situation. Without some time to think about it (such as even looking up what a Spellscar IS) I probably would have said his PC wasn't eligible for Dark Sun play since I had no idea how his powers worked and if they were even possible in Athas. He would have had to make a new one, and delayed the game...something which would have satisfied no one. Instead, however, we were able to look up Spellscars and toss some ideas back and forth how exactly it worked in the Dark Sun universe. (Long story short, it was because a Sorcerer-King cursed him years ago.)
Another way this shared character-building is helpful is when it comes to planning his backstory! Initially when I asked him what his character did, he had some vague idea of being an old (really old) wandering nomad, with magic powers because of "a curse". And he had a giant (medium-sized) pet Raven that also served as a mount.
This was alright, but other than the raven, it's pretty bland and lacking in specificity and hooks. And the raven...WTF. How the hell would this fit into the story? But don't get me wrong - this is a great time for a DM, as you can take what your player has in mind and not only enhance it, but also enhance it in a way that it will flawlessly fit into your campaign. And by doing it together, cooperatively, it's still HIS backstory...you just helped steer him to the final version.
I proposed some different ideas, and after discussing them a bit, throwing some out, modifying some others, his character became a nomad who wandered between city-states as a special courier, riding his Raven mount (keeping his close connection to the Raven.) We also decided that the reason his arcane abilities have not gotten him locked up, enslaved or killed by a Sorcerer-King (SK) is because he is actually doing the SK's bidding, by serving as a guardian to the SK's favorite, exotic, last-of-its-kind pet...a Dire Raven. The Raven was suffering/dying in captivity, unable to be free and run/fly unhindered, so the SK had to free it. And to ensure that it would be protected, he charged the player's character with the responsibility of guarding it, and "blessed" him with powerful magic abilities.
Thus is this character able to use arcane magic & not be killed by the SK, and it the Dire Raven's need to be free and restless nature also connects nicely to why they are always on the move, living a nomadic life.
From there, we moved on to the sometimes tricky question of why the character is adventuring. Fortunately, we quickly came up with a great reason - to find some way to restore lost youth. The character, and the Raven, are now both quite old and nearing the ends of their lives (this also explains why the Raven is only able to serve as a ground mount initially...since a flying mount would be too powerful for low-level characters). The character wishes to find a way to restore himself and the Raven's youth, partially because they are best friends/partners, but also because years ago the SK warned him that if the Raven ever died, he would shortly, undoubtedly follow.
Finally, one other thing that always happens during these brainstorm sessions is that I will bombard him with various questions about what his character would do. From his answers we are always able to really flesh out just who the character is, what he believes in, how he acts/reacts to things, etc. A nice thing about establishing a character's personality like this rather than in the game, is you can take the extra time to consider different options.
During a game session, I would be reluctant to prompt a player with "what if your character did this? or what if he wanted to do this?" because it's almost like I'm wresting creative control away from them. Plus, it is selfish, as the other players are forced to just sit around and wait. But while brainstorming? It's great! Sometimes you will suggest things the player never considered that they immediately latch onto. And the rejection of your suggestions (ie, what the character doesn't do) helps just as much to flavor the blank character as what they do do.
So after about an hour of talking and coming up with cool ideas, we had taken his "cool concept but very unfinished" character to a very interesting, definitely creative person with a great backstory, strong personality quirks AND some great potential story hooks for me to use. He's super excited to play his character, and I have all sorts of evil ideas spinning around in my head as to how I can weave his story into the plot. It's win-win.