Actual legal signals:
- Left Turn - hand out straight to the left (with palm either forward or back (not down or up). I'll often point with two fingers to help convey the message.
- Right Turn - hand out straight to the right; mirror of the left turn. Or left upper arm out straight and forearm up straight. The hand out straight to the right is less likely to be mis-interpreted by somebody that didn't learn the signals, and either form is legal on a bike. In my state (California), on a cycle or motorcycle, either version is legal, but I think there's some states that only legally have the left-arm version of the right turn signal.†
- Stop (or slow) - Left hand straight down with palm flat.
Commonly recommended but not necessarily exactly what the law says:
- Merging - Point at the lane position you're merging to. Looking over your shoulder in the direction you're going to merge can also help make drivers aware you're planning to merge. Or point straight, the same as with a turn.
- Straight forward (at intersection) - point forward.
† In most of the US, left hand straight up (palm forward) and upper arm straight to the left to signal a right turn is a legal alternative or the legally preferred signal, but many drivers will misinterpret it. I highly recommend using the right hand straight out to the right version (either with palm forward or pointing with your fingers), since many people are either unfamiliar with the left-arm-straight-up signal, or misinterpret it (perhaps even as a rude gesture).