In reply to sjc:
In the UK I rarely abseil except in extremis or on something like the Old Man of Hoy. However abroad we do a lot of multi-pitch abseiling throughout the summer on Alpine routes and in the winter on icefalls.
Normally unless it's an easy angled slab and the ropes land on a big ledge, in addition to an autobloc (prusik), we've always tied an overhand knot, about 50- 30 cm from the ends of each rope.
I'd never tie the two ends together, if you are doing lots of full length abseils as you'll end up with lots of twist and kinks setting into the ropes, no mater how new your rope is or how careful you are.
As some of the other posters mentioned, if the ends are left free then the kinks will work out of the free ends.
If you and your partner stay alert and have a well thought out and practised system of double and triple checking (buddy checking) what each of you are doing, you shouldn't get a stuck rope as long as you untie the knot from the free end before you pull it down - just make sure you partner is watching what you are doing before it's too late!
Remember that abseiling is probably one of the riskiest parts of climbing, so get into a habit of triple checking (or more!) everything you and your partner are doing.
I've abseiled off a rope myself, fortunately just a few metres off the ground and know of several others that have done the same, with less fortunate outcomes...
BTW the reason the knot isn't tied right at the end of each rope is that if loose, the knot can roll off the end, this has happened to a friend...