(Yvette also posted a reply just as I was about to hit send, I'm going to post it anyway because why not. Apologies for messing up the flow of the thread)
I thought about this for a long time, because both me and my dad are huge hoarders so we've got loads of stuff in the house that'd we'd want to save, so picking 3 is hard. (I'm answering this from the house burning down point of view)
On the one hand, I'm a data hoarder, I never delete anything. If a drive gets full, I just buy a new one, so at first I thought probably my most important drive. The more I thought about it though, everything major is backed up online and offline in a different building, so really losing any of that would be an inconvenience but not so important I consider it a treasure. I realised though we've got a box full of probably thousands of photos, spanning many decades. That would be devastating to lose. We're slowly working on digitising them, but right at this moment that's a long way from being complete. Depending on the size and location of the fire it would be hard to save the whole box (it takes two to carry it), but in a rush I'd try and grab the negatives from it (remember those kids?), so it could be rebuilt. For a more personal item, I've got a fluffy rabbit teddy thing which I've had since I was born. He's currently sitting on my shelf watching over my room, but that'd be one of the easiest things to grab in a fire that'd upset me if the house burnt down. For the final one, there were loads of other memories and things I'd consider treasured items, but for the sake of making this reply more interesting, I'm going to go with something I've got hanging on my wall, which spent about a year in space and got signed by the astronaut who took it there. There's less than 100 of them in the world, and while it's much newer and less sentimental than everything else I treasure, it's definitely something I'd be disappointed to lose.
For the next poster, if salary/location/etc wasn't a concern, what would be your one dream job?