From a UK government website I found the following document (linked from a page about the Highway Code for cyclists).
Signals to other road users (scroll to the bottom for cyclist information)
Essentially there are three signals for cyclists:
- Left arm out - "I intend to move in to the left or turn left"
- Right arm out - "I intend to move out to the right or turn right"
- (Right) arm up and down - "I intend to slow down or stop" (very rarely if ever used...)
In reality you will find only the left and right signalling used by UK cyclists - any other gestures would not be understood by enough other road users to make them worthwhile.
When I'm turning left I put my left arm straight out.
When I'm turning right I put my right arm straight out.
Then I do the Hokey Cokey.....sorry got a bit carried away there.
I vaguely remember from my Cycling Proficiency test that flapping your right arm up and down signals that you're stopping, but in the more than 30 years since I passed it I don't remember ever using it.
I use all four official hand signals when cycling. This is in the UK of course.
Turning left: Left arm out.
Turning right: Right arm out.
Slowing down or stopping: right arm out, palm down and waving clearly up and down.
Going straight across (for junctions): Right arm bent out at the elbow with hand pointing up.
In Canada, It's
Left Turn: Left arm straight out.
Right Turn: Left arm bent up at the elbow.
Stop/slow down: Left arm bent down at the elbow.
The right arm isn't used because it's harder for drivers to see. I thought the rules were pretty universal. But according to @Amos, they aren't.
Actually, In the UK, I assume it would be reversed to use the right arm, sing you ride on the left and side of the road.