First place to start is listing the stuff you own. I have mine on a Google Docs spreadsheet, with tabs to categorize it. I can access it even if my computer gets stolen.
This will be useful for the insurance. Insurance won't replace anything, just pay you some, so prevention and common sense is really the key:
Securing the points of entrance, adding deterrents such as cameras and sirens, neighborhood watch, random lights and music, not publishing when you're going to vacations in the social sites, having your mail redirected or picked up, having a large mailbox big enough for parcels, automated shutters, etc.
Store your documents offline, like a scan of your passport and important papers. Digitalize as much as you can: I have ripped all my CDs and have a backup at my family's. I started ripping my DVDs too, although it's too big for backups. But at least I won't lose too much if someone steals my CDs or DVDs. Try to rip the most valuable ones, or the rarest.
It's really too bad that with all the technology around, there is no world standard for home automation and security.
It makes the whole thing far too complex to setup for the average joe.
Lol at all those who keep repeating dogs and guns, like the former is an option in an apartment, or like the latter is useful when you're away to anything else but getting your gun stolen too.