The different types of homeowner's insurance policies are designated by what is called an "HO" number, which stands for homeowner. HO-1 was the standard policy for homeowners for a while because it only covered damage types like fire, lightning, smoke, vehicles, aircraft, vandalism, riot, theft, hail or a windstorm, an eruption from a volcano, or damage by glass. Because it is so limited in its coverage, HO-1 is being phased out in general by many states, and is no longer the accepted norm.
Getting into HO-2 will get you more coverage in addition to what's in HO-1, including damage from pipes and plumbing having to do with leakage or freezing pipes. HO-2 will cost you more than HO-1. HO-3 is different from the other two is that it will cover all except the specific dangers. Looking at the policy in detail from your insurance company will give you an idea of what kinds of things it will cover.
For coverage involving property, and not covering buildings, look into HO-4 and HO-6. These are more of policies for condominium owners and renters, and they generally have liability coverage.
The most detailed insurance policy out there is the HO-5 policy. This is a bit more expensive than an HO-3 policy, but it covers things like jewelry, antiques, irreplacables, etc. You can also get coverage included for sewer backups and building code upgrades. Most people feel that getting this "combination" policy will end up being cheaper in the long run than getting a lower-end policy and adding the extras.
The main thing you want to keep in mind is that this is just a guideline as to the differences in policies. Each insurance company has its own little quirks, so be sure to review their variations in great detail to make sure you're getting what you wanted in a homeowner's insurance policy.