Your helmet is your single most important piece of safety gear.
Shapes
There are a few shapes of street helmet: half helmets, 3/4 helmets (aka "open face"), full-face and modular.

For maximum safety, wear a full-face helmet. About 35% of head impacts are to the chinbar area, so you should wear a helmet that protects your jaw.

This helmet graphic shows the chance of an impact in each area.

Modular helmet with the chinbar raised.
Modular helmets have flip-up chinbars that can be useful for riders who need their face to be easily accessible at a stop (e.g. police officers conducting traffic stops, riders in very hot environments drinking water). The tradeoff is the chinbar hinge is a potential weak point compared to a full-face. Some safety standards do not certify modular helmets for this reason. Unless you have a specific reason to use a modular helmet, prefer a full-face.
Safety Ratings
There are a few safety ratings used for helmets:
- DOT (FMVSS No. 218): This is an outdated and poorly enforced US government safety standard nearly 50 years old. If you ride in a US state that requires you to wear a helmet by law, you will need a helmet that passes this standard and has the appropriate sticker on the back. It is otherwise a junk rating. Unlike the other standards in this list, DOT does not require random independent pre-production testing, and independent post-production tests have found 30-60% of DOT rated helmets fail to meet the standard. You should not buy a helmet that has only a DOT rating without one of the others in this list.
- Snell (M2015, M2020D, M2020R): These are standards for racing-oriented helmets created by the Snell Memorial Foundation. Earlier versions of this standard such as M2015 were considered a much better alternative to DOT. However, the M2020D and M2020R standards have not kept up with current medical knowledge and are therefore inferior to the newest ECE and FIM standards.
- ECE (22.05, 22.06): These are standards for general-purpose motorcycle helmets created by the United Nations Economic Commission for Europe. These standards are required for motorcycle helmets sold in most of Europe and are based on current medical research. The 22.06 version of the standard is an especially good one as it includes testing of rotational head injuries.
- FIM (FRHPhe-01, FRPHhe-02): This is a standard for helmets used in racing series organized by the Fédération Internationale de Motocyclisme. This is the standard used in MotoGP and Superbike racing. It is based on current medical research and includes testing of rotational head injuries. The FRHPhe-01 standard is similar to ECE 22.06, with some minor differences. The FRHPhe-02 standard is an evolution with more specific testing for skull fractures and acute hematoma, and is the safest helmet available. These helmets are typically very expensive and not sold at most retailers. Note that only a few sizes of a few specific models undergo certification.
In summary:
- FIM FRHPhe-02 is the safest helmet standard, but not widely available to consumers.
- ECE 22.06 is a great standard for street helmets with wide consumer availability at all price levels.
- FIM FRHPhe-01 is for racers; street riders should look for ECE 22.06 instead.
- ECE 22.05 and Snell M2015 are old standards and should not be considered for new purchases.
- Snell M2020D and M2020R are weird standards created for industry politics reasons and you should ignore them.
- DOT only: Don't. Just don't.