I've been reading "The Merchant of Venice" this week, the first time I've read Shakespeare in a while. What really struck home was the way he scatters brilliant asides - clever lines that aren't strictly necessary, but give the audience something to consider in addition to the main plot and themes.
Here are a few examples, just from the first half of one play:
"I can easier teach twenty what were good to be done, than be one of the twenty to follow mine own teaching." I, ii, 16-19
"I like not fair terms and a villain's mind." I, iii, 81
"... For lovers ever run before the clock." II, vi, 4
"All things that are, are with more spirit chased than enjoy'd." II, vi, 12-13
"... I fear you do speak upon the rack, Where men enforced do speak anything." III, ii, 32-33
Other drama sometimes manages this trick, but often the words of wisdom are culturally specific (e.g. "... don't make fun of grad students, they just made a terrible life choice," from The Simpsons). Shakespeare's insights are much more universal.