I spend most of my time outside the big subs, so here's a partial list (sorted by number of subscribers, from most to least):
/r/explainlikeiama (96,400 subs) Sort of like /r/writingprompts but with weirder challenges. Often too weird to be answered, but every once in a while somebody hits one out of the park. Check the "top" tab, or read this.
/r/calvinandhobbest (96,000 subs) my daily hit of favorite childhood comics
/r/casualconversation (63,200 subs) my nominee for the calmest, most pleasant sub of its size. Although /r/hockey is pretty cool, too.
/r/defaultgems (38,300 subs) a "best of" for comments from the default subs, the comments don't recycle very quickly but it's worth checking up on.
/r/RedditThroughHistory (39,200 subs) Ok, what would people post to reddit if Reddit had been around way back when? Comments and posts about how "those crazy Wright brothers will never get their toy off the ground anyway" and such.
/r/badhistory (37,300 subs) sort of the child if /r/facepalm and /r/askhistorians had offspring together
/r/marijuanaenthusiasts (32,900 subs) This is not what you think. It's a sub for arborists. The subscription number is, I think, inflated by the number of /r/trees subscribers who like the in-joke nature of those two subs.
/r/cyberlaws (21,800 subs) a recap of what laws are in place, proposed or changed that regulate the internet
/r/nongolfers (18,900 subs) Inspired by the famous NdGT quote comparing being an atheist to being a non-golfer, this sub is relentlessly a-teeist, and euphoric about it!
/r/suggestmeabook (15,100 subs) was born when the mods of booksuggestions went insane and alienated their user base. It's just what is sounds like. Good quality advice.
/r/EAF (13,000 subs) Epic As Fuck - only one or two new posts a day of anything that is... well, what the title says.
/r/scams (5,400 subs) People post about common scams, ask if they are being scammed (usually the answer is yes), and get advice about how to deal with being in the middle of a scam. This sub could really use more subscribers. The issue is fascinating.
/r/bestofreports (2,400 subs) where moderators of reddit share some of their most favorite/silliest reasons given in reports
... and a bunch more. Reddit quality is in the small subs, I think, not the larger ones. Although /r/AskHistorians is the most informative sub I know of. Still, the mods have to have all the patience, forgiveness and understanding of Attila the Hun to keep the quality up.