Series: Highest output, warmest tone (bass and mid emphasis), hum-cancelling
Parellel: Lowest output, brightest tone (treble emphasis), hum-cancelling
Single coil: Slightly higher output than parallel, slightly less bright tone (though still noticeably brighter than series), not hum-cancelling on its own (might be if you combine it with other pu's)
In addition, choosing either coil in single coil mode gives you slightly different tones. For example, with MM pickups, the coil closer to the bridge gives a tone which is very similar to a bridge jazz pu, while the other one keeps more of the MM character. I have a Basslines MM pu in my main bass with all three options: I use parallel most of the time, switch to series for soloing and select single coil if I want that bridge jazz tone, or to combine it with the neck jazz for a great hum-cancelling tone that I use mainly for walking lines.