stiff gears and chain coming off while pedalling forward (hub gear) So I recently replaced the back wheel's tyre on my bike. Got it all fitted back on again, and the chain and everything are in place as they should be. However, changing up gears has become very stiff indeed, and as soon as I get on the bike and start pedalling, the chain snaps off from the wheel and wedges itself in a gap.

No idea what the cause is - I slip the chain on by pedalling it a bit indoors (without sitting on it), but as soon as I get it outside and peddle for a second, it comes right off. The bike is about 10 years old, hasn't had much use until the last few months (when I've been riding it every day), and had never seen any reparations until I replaced the back tyre.

I'm fairly sure I've messed something up while putting the tyre on. I don't really know much of the terminology (wikipedia calls my gears 'internal hub gearing'). The gears seem to be attached to the wheel itself, rather than the bike frame (which seems different to the videos I saw on the internet), so I had to remove the chain and unhook the gear changing wire thing from the wheel to remove it.

Sorry for the vague information - anyone got any ideas?
There could be a few different issues:


It your Rear wheel is sliding around in the rear dropouts and you wind up loosing tension on the chain or screwing up the alignment of the rear wheel. It's really a common thing on bikes with horizontal dropouts, which I assume your bike has.  When you start to pedal, if the rear wheel bolts or quick releases are not tight, then the wheel can slide forward in the dropout, the chain comes loose and falls off. Try tightening bolts or quick release tighter or use a chain tensioner or tugnut to help prevent the axle from slipping.
Your chain is really worn and/or your cogs are very worn, this causes the chain to skip off the front chainring or rear cog. See Sheldon Brown's site about chain wear to diagnose this issue. 
You have a bad chainline.  Instead of going from the rear cog on the wheel to the front chainring in a straight line, it bends the chain diagonally, causing it to hop off the cog or chainring easily.  This may be due to spacers incorrectly placed on either side of the rear axle. Credit @DanielRHicks
The chain could just have too much slack, try pulling the wheel back and resetting the tension tighter.
Bent chainring causes chain to jump.  Spin the chainring without the chain and see if it 'wobbles', if so this could be causing your chain jumps and the chainring should be replaced.