Where can I go online to learn about a building, based on its street address?

try http://www.zillow.com. That should do it!

Not sure you’ll find anything about who once lived there, it will tell you about the building.

I would check the locality’s property assessment website. For example, I was able to find this about an apartment I used to rent in Pittsburgh.

More generally, there's RealQuest and Google Base for Housing.

Also, EveryBlock is pretty good for finding civic goings-on in SF, NY, and Chicago, but this is on the block, not building, level.

Zillow only has residential homes, right? I’m looking for information on buildings that might be commercial or otherwise zoned.

Which locality are you interested in? San Francisco? Try SFParcel (warning: the user experience is about what you’d expect from a government website). It includes commercial, as well as residential, buildings.

Most big cities have a site similar to this one.

Check your county recorder’s website. A lot of them are putting plats and tax records online now. They can be very revealing.

For New Yor City addresses try the Dept.of Buildings

Philadelphia – http://www.hallwatch.org