Also Gem from the episode "The Empath." She never speaks a word, and all you see her do is take peoples' pain away like E.T.
Also, also, Jame Finney, the teenage daughter of one of Kirk's friends and a very emotional Shrinking VioletPettanko with blue eyes big enough to drown in and a pleated miniskirt that screams "schoolgirl". When she apologizes to Kirk so sheepishly, you just want to give her a big hug.
In Densha Otoko, the eponymous character's otaku friends mention the word "Moe" in front of Hermes, and Hermes, who is a normal human being and does not know what the word means, asks them, "Moe?" The friends think this is so Moe that they record her saying it.
Small Wonder, a show about a Robot Girl living with her inventor and his family and making their lives a mess while being innocently cute. A rare American example of the theme.
Lexie Grey (aka: "Little Grey") from Grey's Anatomy. Yeah, the one with the juice box... Not a virgin, but about as pure as a character can get on that show...
To an extent Doctor Who's Jo Grant and Polly cover this territory at times.
Also, Amy Pond and her husband, Rory, who is adorkable in human form.
The Doctor himself is sometimes this, especially his Tenth incarnation. It went Up to Eleven in his Eleventh incarnation, who was basically a big, overgrown puppy in human form.
Victoria and Zoe definitely fit into this category too. Victoria has the appearance of a Disney Princess with her huge eyes and blushing, fragile seeming Victorian era manner and appearance.
Spencer Reid from Criminal Minds. Conspicuously the youngest member of the BAU, Reid's adorableness is frequently signposted by Matthew Gray Gubler's voice jumping an octave and random characters flipping his hair. The writers once devoted the first two minutes of an episode about another team member's grave childhood trauma to Reid performing "physics magic" with utter joy.
Zack Addy from Bones should count too. He was the young, innocent and socially awkward member of the squints (forensic geeks) and was like the little puppy of the team. Everyone loved him, sometimes more than the two main characters.
For a male example, we have Trip. Appears younger than the rest of his teammates (his actor, Kevin Kleinberg, was 17 when he got the part), has mild cloudcuckoolander tendencies, is really good with tech, his innocence once led to him falling for a villain's plan, and, most importantly, he is downright adorable◊.
Annie Edison of Community. When an argument makes her bring out the Puppy-Dog Eyes, everyone else (except Jeff) has to close their eyes to avoid instantly forgiving her.
Abed should also count, him being socially awkward and weird, not helping on the fact that he appears to be rather young(early 20's) everyone in the group seemed to look out for him, or at the very least not target him when they get into a fight, a lot of girls also ended up getting crushes on him do to finding him adorable and his aloofness reminding them of their dad.
And even moreso than Emma, Kurt. If you took all the most adorable traits a twenty-year-old guy could possibly have and smushed them all together, you'd get Kurt's actor Chris Colfer.
Brittany! Her childish nativity and sweetness is an ungodly cute combination.
Howard's girlfriend Bernadette from The Big Bang Theory. Seriously, she's a short, adorable blonde who wears glasses and has an incredibly cute voice, she's like an assertive live-action Mikuru with slightly smaller breasts.
Parker, from Leverage. Partially as a result of her obviously Dark and Troubled Past and partially as a result of her endearing Cloud Cuckoo Lander qualities, Parker's emotional pain seems to set off protective instincts in the entire team. Eliot even offers to kill a charlatan psychic for making her cry.
And Eric Matthews. Amazingly, another example of becoming more Moe when he's ''Chantelle'' in What A Drag (S7 E11). She's so sad when she is told that she's ugly, she actually cries for days until Topanga (not knowing Chantelle is Eric) says she has 'a beautiful spirit' after she gives her good relationship advice.
Peggy Olsen on Mad Men; even when she becomes successful, she's just so damn adorable, you want to hold her in your arms and never let go.
Ambassador Delenn from Babylon 5, despite being one of the most powerful sentient beings in the galaxy and more than capable of commanding a war fleet, can turn absolutely kittenish. Witness her private moments with JohnSheridan, or any time she embarks on a passionately idealistic speech. This fits with her role as The Heart, as she is easily the most dreamy, romantic character on the show. Mira Furlan's dreamy green eyes don't hurt, nor does the fact that her nose goes all adorably wrinkled when she's confused or smiling.
Joshua from Dark Angel is an unexpectedly adorable Moe. Maybe not in appearance, what with him being a seven-foot mutant dog-man. However, his sweet, gentle, idealistic personality and tragic story leave many just wanting to give him a big hug.
Rather surprisingly, Benedict Cumberbatch's performance as a very young Stephen Hawking in BBC's Hawking inspires moe feelings in the female fanbase, at least if the comments on youtube and tumblr are at all indicative.