Here are a few tips and techniques that I have discovered and found useful.

Another use for needlefelting!
 
I had read about needlefelting being used to darn socks, and wondered if it could be used to repair a very old, tattered and torn stuffed rabbit of mine.  "Bunny" (well, I named him when I was a toddler so originality wasn't high on my list of priorities) is a very old toy - as old as me.  He had lots of holes which I had repaired very inexpertly by stitching countless times, so many times that they had become unstitchable and I thought I might have to patch him with fabric.  Then I wondered if I could needlefelt over the holes.  I tried it and it worked like a dream!  Bunny has been given a whole new lease of life - he isn't losing his stuffing any more.
So, if you have a much loved but rather holey teddy bear or stuffed animal, try needlefelting over the hole.  Just place some wool fibres over the hole and needlefelt from all angles until the felt forms a "skin" over the hole and is firmly held in place around the edges.  The trickiest bit will be finding wool fibres that more or less match your teddy - in my case I had to use white wool to patch very faded blue but I think he looks fabulous now.