Why do smoke detectors go off when lightning strikes?

Lightning is a nasty thing. Powerful. Very high current at very short rise time. This causes an strong EMP (ElectroMagnetic Pulse) which will be picked up by anything conducting. A 1m free-hanging wire may create a voltage peak between its ends. Even short connections may see spikes. Decoupling doesn't always work as the EMP can enter an IC directly; it doesn't have to come by the (power) wires.
So no wonder some products experience a temporary malfunction during a lightning bolt, and high impedance mean more sensitive. If the disturbance remains within the device's voltage range it may behave wrongly without suffering damage. Higher voltage spikes may destroy (parts of) the device.

I heard the story of a Dutch family where lightning had struck in the backyard. Every electronic product in the house was fried, from TV and PC to cameras and mobile phones. Se non è vero...

And David with his smoke alarm network/antenna, well... :-)

Just to add what the other folks have said... The fire alarms in my house are all inter-connected. When one goes off, they all go off. There are wires inside the walls/ceilings that connect them all. Those same wires, because they are long and unshielded, are excellent antennas and would easily pick up the EMI from a lightning strike. Also, the signal on these wires is very simple and the electrical noise generated could easily fool the alarm into thinking that some other alarm went off and so it should too.

What the other guys said could also be true (except the part about CO2 setting off an ionizing detector, it is actually a smoke particle that does it), but if the alarms are interconnected then that would be the weakest link. It's much easier for EMI to get into a 50 foot wire than something that is about an inch long.

I think ionization and EMP glitches are missing the point. I find ionization in particular very hard to believe. How is lightning 100s of meters away going to ionize the air in my smoke detectors pretty much at the same instance as the lightning? It's not. I don't believe the EMP theory either. The pickups are sensitive and high impedance, but also shielded from external capacitive pickup. If not, ordinary power line hum and nearby static discharges would set them off, but they don't.

What is really going on is that the power got glitched. A lightning strike makes a mess of the power line for a few 10s of milliseconds. Most smoke detectors, including all the ones in my house, sound off for a short time whenever the power goes out. They are fairly sensitive to this, more so than most ordinary appliances. You may notice a small flicker in the lights or a glitch on the TV at the same time (although lightning causes TV and radio glitches by other means too). When we have a pure power glitch not caused by lightning, it is always the smoke detectors that exhibit the symptom first. Most appliances can take a cycle or two of missing power, but the smoke detectors seem to be the most sensitive. I don't know if this is deliberate or just a byproduct of their sensitive detection circuitry.