Is it good to auto-attack your own creeps?

This would help to bring them closer to your tower, which I'm sure is a good thing. However, I've never seen anyone do this. Am I missing something?

I do, sometimes: the problem is that you might give easier last hits to the enemy laner if you don't time your autoattacks well, plus a lane pull from a support usually denies a lot more experience (so it's negligible most of the time). And also, if you're too close to the enemy tower, you might expose yourself too much and become an easy target for ganks.

Well you might already know this, but remember that you can only start attacking your own creeps when they fall below 50% HP. So you can't just attack them all the time.

I tend to do this a lot, especially if I'm playing a Flash Farmer, but don't want to push the lane with my Skill, e.g. Dragon Knight + Flame Breath. It is useful to have a Support do this instead, but if they don't need to be in your Lane, it's best for you to soak up Solo Exp and make the occasional Deny yourself.

The one bad habit I notice when I do this though, is that I sometimes miss Last Hits in favour of Denies, which isn't really worth it 8{(

You also have to be careful that you're not constantly pulling the Creep Wave under your Tower, or you may end up Pushing the Wave anyway.

Pro Tip : Attacking your own creep (or any allied creep) in range of a tower will cause it stop aggro-ing you and change target. (Even if its full HP).

Think about it, both creep waves are just at strong, so in theory the creep line, the place where they meet shouldnt change. Unless ofcouse you damage the wave. If you put damage into their wave it will mean that you will push, so for every point of damage that you do to the wave, you should also do to your own if you want to wave to stay in the same position.

If you want to keep the lane back, make sure you attack your own creeps, and kill your own range creep fast, since it has the highest DPS.
Dont screw with creep aggro too much by right clicking their heroes. Becouse if you do that the enemy creeps are attacking you and not your creeps, and as a result your wave will push,

as pretty much every1 already said its a good way to control your lane or to manipulate the creep-equilibrium. If you want to fight closer to your own tower, try to deny them earlier (hitting them multiple times), if you want to be farther away from your tower (if you are sure, that you will be pushed under your own tower - were lasthitting is harder - next wave for instance) hit the enemy creeps some more ...before last hitting ofc.