Darker Atomosphere for Sonic if it's actually done well. Sonic Adventure 2 is the only game IMO that got the darker atmosphere right without it feeling too out of place or feels like I'm playing a whole different franchise with Sonic characters staring in them. Shadow the Hedgehog in Sonic Adventure 2 is 10x more badass then the one in the Shadow game and he haven't cussed or use any kind of weapon. Sonic 06 is a complete mess overall.
Oh, yeah. While I did like Shadow's darker atmosphere, they did go pretty overboard at times where it just became Narmish. Adventure 2 probably is the best example of a darker atmosphere, actually.
Adventure 1 and 2 struck the right balance in terms of dark-and-serious-but-not-too-dark-and-serious plots, as far as I'm concerned. The rest either falls into 'barely existent light hearted fluff' or 'dark for the sake of dark'.
Admittedly, I would say that even Sonic 06 wouldn't have overstepped the mark, were it not for the horrid 'realistic' style and the fact the plot and game in general were just a mess. Visual style aside, tone-wise the plot wasn't much darker than the likes of the Adventure games, at least not to the comically blatant extent that Shadow was.
I don't like Sonic games and plots being overly dark (read: SatAM), but at the same time I want them to be substantial enough and serious enough for me to be able to actually invest in them and enjoy them. Of course, it's all about balance really, and let's not forget that 'serious' doesn't have to mean 'dark'.
EDIT: Apologies in advance if this offends anyone, but from my experience I've found that most people who want Sonic to be 'dark for the sake of dark' generally tend to be 12-15 year olds who are at that awkward stage where they still like something 'for kids' despite peer pressure telling them that they should grow out of it and therefore blame the series for not growing up with them (or if not blaming, at least wishing it would) because they're at a stage where they feel insecure with themselves about liking something that's primarily for children. Of course, by the time they hit around 18-19, they've realised that peer pressure sucks and it's cool for them to like what they want to like regardless of the target demographic.
Seriously, the number of Sonic fancharacters you come across with horrifically emo pasts involving drugs, abuse and teen pregnancy is hilarious. Because, you know, that totally fits in with the Sonic universe, am I right? 
Oh, man, hell no. I'm not talkin' about that fan character shit, that's just not right. But yeah, I agree, it's a lot about balance.
Sa2 and Sa1 somewhat was they closest they ever got to doing it right and I'm still not crazy about it (Sa2 at least).
Games like Heroes, Unleashed, and Colors which are much more lighthearted in nature,tend to be more unique and have its own charm and general atmosphere to it something that you can call SONIC, that's what I want to see more of.
It's perfecttly fine to have dark elements every now and then, as long as it doesn't take over and mutates the series into something it's not like Shadow and 06.
Personally, while I agree Heroes, Unleashed, and Colors tended to be more lighthearted, I wouldn't say that's not the only thing Sonic can be, though I do agree it shouldn't like overstep it like Shadow or '06 did.
The content and execution of the plot, dialogue, character animations/gestures and interactions, as well as stuff like environment construction and music/sound design are far more important to me than the tone of the game. I want to be invested in the plot, with the darker themes to come through underneath. A layered narrative if you will. Visuals, sound, dialogue and all the stuff mentioned above are far more important to delivering a more potent and memorable narrative.
As long as the stories never, ever, EVER retread the steps of Shadow and 06. The former of the two was the pinnacle of immaturity in Sonic games. The latter was confusing and generally terribly written.
I agree with the layered narrative idea. Darker stuff coming through underneath would probably be a good way to get a darker atmosphere into Sonic. Also, about Shadow and '06, I know the stories were outright ridiculous, but to be fair, parts of the darker atmosphere seemed pretty enjoyable, though. It's weird, but you can like the atmosphere of something without liking the story.
A darker atmosphere for Sonic wouldn't necessarily be bad, given some good, recent attempts of it in games like Unleashed, and the Storybook games. As for ShTh, and 06, I don't think those two games are very good attempts for a darker atmosphere for Sonic. ShTH had some good moments in it, with some good humor to lighten up the tone (one slightly memorable line from Shadow in that game, is that one line he says when taking the Chaos Emerald from Sonic's ship thing. Something about candy.), although those good parts of ShTH were marred by the bad parts of ShTH. As for Sonic 06, it took itself way too seriously, to the point where it could almost be considered laughable.
Sonic Unleashed, however, brings a brilliant atmosphere with some dark elements alongside it. In contrast to ShTH and 06, Unleashed's atmosphere is a lot more enjoyable. For Sonic at least, I'd love to see a darker atmosphere not unlike Unleashed.
I believe the quote you're looking for is the ol' "taking candy from a baby" cliche. Anyway, I think Unleashed came off a bit TOO bright in the early parts of it and Chip actually proved to be detrimental to the atmosphere by being completely annoying any time he does something, sometimes even in light-hearted scenes.
