How many pads do you bring when you go bouldering?

I suspect it varies by group size, pad size, and the location, but assuming that it's you and a friend at a typical spot... I can't figure out if I'm just not confident in my spotter or whether I actually don't have enough padded surface area...

Two. A metolius magnum and a mad rock Madpad. The Madpad frequently goes unused though.

As you stated it totally depends on the area and the landings. I find that bringing two full pads and a half pad (stuffed in a full pad) is usually enough for me to feel comfortable; and easy to lash together and carry to far off boulders if need be. I often boulder alone and 2.5 pads, more often than not is enough for me to not hold back because of no spotter.

I take an Organic Simple Pad most of the time for most places, but if I'm working highballs or problems with bad landings I'll take my Organic Big Pad instead. Minimizing impact on landing zones is smart because erosion and clearing landings too much is starting to cause access issues. Just finished touring around 8 spots around Portland Oregon/Columbia River Gorge & Smith Rock with only an Organic Briefcase Pad and had no problems with practically every route, even with crappy talus filled landings. Confidence and quality of the pad make the biggest difference in my opinion.

It really just depends. A big organic is usually plenty for a climb that has a flat landing and is of average height, but if the landing is bad, even 10 pads might not be enough e.g. Luminence.

As many as you need. Sometimes I go out with 1 pad, other times I've gone with 4 strapped together including 2 jumbo's. Depends on what you're climbing.