Trello is fantastic, but now I'm worried that I'm too dependent on it and I should arrange an offline alternative.
Take my money, Fog Creek.
If this is the kind of problem that excites you, we're hiring :-)
Sadly the better implementations I've used myself (or have heard about) are not publicly available. The closest thing in semi-widespread use seems to be Zookeeper, but it's more like Oracle when you really wanted SQLite (standalone service vs. library).
There is also a print option, but that doesn't seem to print the back of the cards so it's pretty useless, unless I'm mistaken.
In my experience, what self-hosted bug-tracking systems might gain in redundancy (a few hours every time a major storm hits) they lose to context switches (which hit team morale, not merely time.)
"Hey, Bob! Can you reset the MySQL server again on the bug-tracking maze set up by Fred over 4 years ago?"
Bob obligingly does so, and then, having been interrupted in the middle of a hard problem, loses his place and can't get back up to speed by the end of day. So while you may gain four hours of butt-in-seat time, you're losing four hours of real productivity on a far more frequent basis.
I'd rather pay Fog Creek to worry about that stuff, and actually ship products.
I do hope at a better time, Fogbugz can consider redundancy/failover that Stack Overflow enjoyed.
Frankly this is just making us appreciate Fogbugz all the more since tracking our time without it will be a real PITA.