If the base resistors are too small both transistors will turn on and stay on - make them 20 times larger in value than the collector
resistors and the circuit seems to start reliably (and will even run at down to about 0.8V supply! My circuit seems to start up in the
same state every time, for what its worth - I wouldn't rely on this though unless using non-symmetric component values.
The capacitors see about the supply voltage across them for half the cycle, then a reverse Vbe (0.7V or so) for the other
half cycle - most electrolytics will tolerate this small reverse voltage but its not recommended.
The name for all oscillators of this sort is "relaxation oscillator" - there is a sudden change, then an RC (or RL) circuit discharges
or charges (relaxes...) and then suddenly a new flip in state happens. Positive feedback causes the sudden change in state, which
saturates, then the relaxation phase before the next positive-feedback step can happen. The classic 555 timer circuit is another
good example of a relaxation oscillator.
[edit: just for completeness, I'm using 2N3904's, 4k7 on collectors, 100k on bases, 10uF non-polarized electrolytics.
Runs with a period of about 2.0s at 0.8V, 1.6s at 5V and the rapid switches have a 100ns rise time or so.]