There have been an awful lot of types of arrow in the comics, ranging from obvious to silly.
The movie showed him using:
Conventional sharp or piercing arrowheads (pretty much all kinds)
- Side-firing/area-effect-shot arrowhead (not seen in the comics, although similar to some that are)
- Explosive arrows (in the comics he's also used 'thermal' arrows with blasts hot enough to melt metals)
- Bridging line/cable/zip cord arrows
- The hacking-module arrow (which was original to the movie as far as I know; it's more sophisticated than anything in the comics)
The following list have all been used in the comics at some time. (List based on his character sheet in the 90's Marvel RPG; it was pretty comprehensive at that time. As the comics damped down on the silly-arrows list after that period, it includes everything he's used since then that I know of.)
- Blunt-tip (for when he doesn't want to puncture anything)
- Acid arrows
- Bola and Net arrows
- Boomerang / ricochet arrows
- Electrical arrows (essentially a taser on a stick)
- EMP arrows
- Firefighting foam arrows
- Flare and flashlight arrows
- 'Nullifier' energy-damping arrows
- Rocket-assisted arrows (for that extra range...)
- Smoke arrows
- Sonic arrows (essentially the noise part of a flashbang; since he's nearly deaf in the comics, he can make good use of this)
- Tear gas arrows
He's also had Adamantium and Vibranium arrows in the past. (Yes, really. But he saved them for emergencies.)
He's also used some alternate arrowheads designed to stick to other surfaces; these are often combined with other arrow types, especially the zip line:
- Magnetic arrowheads (also used as improvised EMP disruption)
- Putty arrowheads
- Suction-cup arrowheads