Once you've been robbed of (or merely lost) your documents you'll have to do something about replacing them. First step:
Police! Lots of chocolate! Second Step: Police!
I wasn't exactly sure where or how to report crimes in Bogotá (and to be completely honest, I forget their equivalent of 999 about five seconds after I look it up. For future, and hopefully entirely unnecessary reference: 123). Thankfully, while I was stocking up on comfort food I found a pair of police officers. They were incredibly kind and helpful - not only telling me where to report the crime (just around the corner - phew!) but also regaling me with tales of ingenious pickpockets, the various times they'd been pickpocketed themselves, and just being nice and sympathetic in general. Feeling much less tonta (after all, if the police themselves get pickpocketed, I shouldn't feel bad about it happening to me!) I strode off to the police station where another pair of officers were outside. I'd arrived exactly at closing time (6pm) - noes! However, continuing the trend of lovely police officers one dashed inside to check that the relevant desk was still open, and came back saying that as I'm a foreigner (I strongly suspect he used a different word to the lady inside) they'll stay open five minutes just for me.
Inside I was escorted to a comfy chair where a gorgeous lady with guns on her lapels (really not confidence inspiring to someone who's heard this story) took my details and gave me a form. In the end we decided to say that I had simply 'lost' my documents, as that form takes a matter of seconds to fill out and can be used immediately to apply for a new ID card. Actually filing a criminal complaint can take several weeks before you get to the point of being given useful papers, and besides, I really wasn't paying attention to the thieves so would be useless as a witness.
All in all, visiting the police when you've been robbed is a really good idea. Not just because it's useful, but because they're all really good at cheering you up!