Spider-Man, especially when still a teen like in the Ultimate verse. Apt to start geeking out about the science behind whatever villain that week is using, and he trips over himself in social situations a lot. Still he goes out and does the right thing because it is right.
Clark Kent, more so Post Crisis (where his moderate dorkiness is natural) than Pre Crisis (when his extreme dorkiness was just a facade).
Kid Devil is the single most adorkable Teen Titan, thanks to his geeky love of comics, superheroes and movies, and from usually being the underdog.
This is probably a big reason why fans love Ted Kord/Blue Beetle II so much. His successor, Jaime Reyes, shows it too, especially in Batman The Brave And The Bold.
Dan Dreiberg/Nite Owl II of Watchmen is based on Ted Kord, and therefore also fits. It doesn't hurt that he and his Love Interest Laurie Juspeczyk/Silk Spectre II are, despite the uber-deconstructive nature of the story, the only two heroes in it that would fit in in a "normal" comic just as well. Dan's got some baggage, but it's normal, sane baggage.
Tim Drake's (aka Batman's sidekick Robin) grown up a bit, but he's always been a huge geek and when he was younger was pretty unsure of how to act around girls. But he's still seen as pretty cute, and does end up getting an awful lot of girls.
Superman's pal Jimmy Olsen. He's been the textbook example of adorkableness in comics for nearly 70 years. Artists just love drawing him with that classic sweatervest and bowtie combo.
Peppermint Patty, Charlie Brown, and Linus can have their moments.
Jeff Smax, The Big Guy in Top 10. Though he starts off as being rough and uncommunicative to his new partner Robyn and much of Precinct Ten, he gradually starts opening up, and is even visibly distraught when Robyn is nearly killed and trapped under wreckage by a rampaging perp. It really starts coming out in his own mini-series Smax, when he returns to his own dimension. There, it is revealed that much of his gruff demeanour comes from having No Social Skills whatsoever. He's also intensely embarrassed about his fantasy pastiche world, as well as his incestuous relationship with his twin sister.
Tubby from Little Lulu in spades. He's appeared in his own solo comic stories and earned his own comic series, that you can't help but feel the love for him.
Quite a few characters from Get Fuzzy could qualify, particularly Satchel Pooch, Mac Manc Mcmanx and Foodar.
Bane from Secret Six is a pretty good example, at least when it comes to women. His attempts to woo a woman he has been set up with first amount to handing her flowers while stating "I wish to mate. I have brought the bargaining tokens they gave to me. Shall we begin negotiations?" Then when she compliments his eyes, he replies "...Your hips seem as though they would bear an adequate weight ratio." This is all in between the moments he's stunned speechless by her.
Dane Whitman a.k.a. the Black Knight, especially in Captain Britain and MI13. He's good-looking, skilled, and well-intentioned, but prone to cheesy heroic speeches, corny chivalrous gestures, cracking bad jokes, snorting when he laughs, sticking his foot in his mouth repeatedly, and petting kittens. His girlfriend finds the speeches and gestures endearing, and at one point when he accidentally ticks off his girlfriend's father, said father watches his bumbling attempts to apologize and notes, "It's hard to be annoyed at him. That in itself is annoying."
