Legality of Alternative Headlights

In the USA, headlights are only legal for use on public roads if they are DOT approved. (Similar laws apply in all other "developed" countries and many other countries.) This requires that samples of the headlights be sent to the proper testing laboratory and certification must be obtained that the design is approved. Approval is only with specific bulbs tested in the lab in the samples and DOT approval is invalid if a different bulb is used.
It is illegal to use on public roads homebrew headlights or headlights using a bulb other than what they were DOT-approved to use. For example, a headlight that is DOT approved and normally uses a 9005 halogen bulb is almost certainly not DOT approved for anything else - especially not a D2S for example.
Many HID conversion kits come with disclaimers to the effect of "off road use only". Such disclaimers may appear in the kit seller's ads, web site, or on the kit packaging. Less honest retrofit outfits may merely fail to let you know that such a retrofit is not road-legal. More dishonest retrofitting outfits may even falsely claim that their headlights or ones modified with their product/service are road legal.
DOT requirements have lower and/or upper limits (sometimes both) on candela ("beam candlepower") into many different directions, as in various angles above, below, and to each side of straight ahead. In the unlikely event your headlight meets all of these and other technical requirements, it is still illegal unless it is submitted for testing and certification.
As for what can happen if you use illegal headlights?
1. Often enough, nothing. This depends on location. In some USA cities, law enforcement of traffic regualtions in general is lax. Police are generally not equipped to do headlight photometry anyway.
2. Some unlawful HID retrofit headlights are obvious to a few cops. It is more obvious if you have the really bluish or aqua-ish or obviously dichroic fake HID bluish headlights that are known to some cops to be a safe bet to not meet the complex photometric and colorimetric standards.
If the cop believes you have unlawful headlights, you can be stopped and ticketed. Depending on your state, the violation may be having an invalid inspection sticker or whatever violation of headlight law. Depending on your state and the mood of the cop, you may in extreme cases be barred from driving the car at night (or at all) until it has legal headlights and it has passed inspection again with the legal headlights.
3. Excessive light in some directions can dazzle other drivers. It is possible for you to be legally liable if this causes or contributes to an accident. Modified headlights might have insufficient light in some directions, and you could be held legally liable if that causes or contributes to an accident.
4. You may have trouble with your insurance company if you have an accident while driving a car that cannot legally pass inspection or has fraudulently passed inspection, even if the inability to legally pass inspection did not contribute to the accident. You might also have trouble with your insurance company if you are cited for driving without valid current inspection stickers or are cited for having fraudulently passed inspection.
Note that at least in some states, "off road" lights must be inoperative when driving on a public road. This may mean having opaque covers on the lights and/or having wiring to the lights disconnected.