There seem to be a number of ways that your Apple Watch can become damaged that make it eligible for service, both in and out of warranty. Under the standard one-year limited warranty, for instance, Apple will apparently repair a watch with debris under the glass, or pixel errors. Apple will also reportedly fix a watch were the back cover that has been removed, according to MacRumors:
Apple Watch damage that is eligible for warranty service includes user-claimed debris under the display glass or pixel anomaly, a back cover removed with no damage, and any condensation in the heart rate sensor windows. In particular, the document states that a removed back cover is only covered when not accompanied by enclosure damage or evidence of prying.
There are a number of damage instances that are not covered under the warranty, but are still eligible for service. These are said to include a missing or damaged digital crown, cracks in the display glass, missing band release buttons, and cracks in the back cover.
Apparently not eligible for service are disassembled units or "catastrophic damage", which makes sense, given that it would mostly likely entail your watch being destroyed, and you'd probably be better off getting a new one.
For extended protection, including a two-year warranty and repair for two incidents of accidental damage for a service fee, you could also get AppleCare+ for your Apple Watch.