Sam & Max Hit the Road
Full Throttle
Toonstruck
Grim Fandango
And if you want something a little more serious (as in, not outright comedy, but still humorous), The Longest Journey. You can get it from GOG.com. And the Gabriel Knight and Tex Murphy series, although they might fall below your graphical threshold.
EDIT: Oh yeah, and in case you didn't know, there is actually a Broken Sword 4 (subtitled The Angel of Death), but I've not played it yet.
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"I'm Commander Shepard, and you're standing in the biggest library in Citadel Space. Look me up."