As this topic comes up a lot I'm making a sticky thread to keep the output current chart for the ULN handy. Keep in mind that these are MAXIMUMS and to be safe you should de-rate a bit.
(http://www.efx-tek.com/files/uln2803_spec.jpg)
I decided to measure the chart at the 100% duty-cycle point and came up with these values -- to protect the ULN you should not assume the current values per output, based on how many are running at the same time.
1: 500mA
2: 475mA
3: 365mA
4: 290mA
5: 245mA
6: 220mA
7: 185mA
8: 170mA
The reason for the spec has to do with heat build up in the chip; too much heat and it can pop like a piece of popcorn (this happened to John and me at a recent trade show!).