In reply to CHarrison:
My personal beliefs/assumptions (probably not shared by anyone):
If you are doing a short route you are happy to fall off (with or without pads), you are bouldering. Obviously pads will increase your 'maximum happy height'.
If you climb outside of your happy height into a point where you are no longer happy to fall off, you are no longer bouldering. Bouldering (to me) is about falling off :P
If you are using a rope (and I mean using, not just taking up for the abseil or psychological benefit) you are doing trad. If you are using a boulder pad to protect the start, but the rope to protect the rest, you are still doing trad. Ethical debates may ensure about whether you are doing it in 'good style' or not or whether it is cheating. Personally I am of always of the opinion that falling off and breaking things before the first gear is Not Cool: style be buggered...
If you are not using a rope, and you are above your happy height and are not OK to fall off then you are soloing. If you are doing a 10m problem over a pad, you are likely to be soloing. You may find the pad provides additional safety at the bottom; that is up to you. Alternatively you may be doing a 6m highball problem with a 10m scramble exit at significantly easier grade. I would argue that you have bouldered the problem then scrambled/soloed off...
TLDR: bouldering is about falling off.