In reply to Nick Smith - UKC:
Get out on some routes well within your grade - I mean REALLY easy stuff for you - maybe ones you've climbed before and really enjoyed.
Start running these routes out a bit - get halfway up the pitch and just push it a little bit more than you normally would. Keep practicing this and pushing it a little more til you start to enjoy the freedom of moving above your gear...
I taught myself to lead, but when I ended up on a lead course at the Brenin the instructor suggested to me that, if I felt confident in my abilities to climb the section above me, I should try not to spoil the pleasure of climbing it by stopping to put too much gear in.
(I'm not trying to imply that the PYB instructors suggested I stupidly endangered myself by encouraging me to excessively run out routes - far from it: they rightly suggested that it was my choice to assess risk and make my own decision based on that).
My point being that your confidence to climb above your gear is a skill/technique developed in the same way as any other; it may take a while to develope naturally, or you may need to do some specific training to encourage this.
I found that climbing on easier routes has allowed me to run out and thus enjoy the feeling of exposure that I get from this - from here the step to running out on harder and harder routes is a smaller one than if you just jump in at the top of your grade.
We learn best when we push our boundries and then reflect on the resulting experiences (I think the idea is not to push so far you are a gibbering wreck or otherwise incapable of reflection!). The more you do, the easier it will get, and the better and more confident you will be as a result.