There are manycharacters who are dumb or airheaded. However, for some of these, what they lack in intelligence they make up for in compassion and altruism. The Kindhearted Simpleton isn't the sharpest tool in the shed, but is always well-meaning and compassionate to other characters. Probably will not be quite as dumb as a standard Ditz or as airheaded as a Cloud Cuckoolander, since that is not the focus of their character.
Due to their well-meaning nature but below-average intelligence, these characters have the potential to be taken advantage of and manipulated by smarter (and occasionally evil) characters. The Kindhearted Simpleton should beware of Manipulative Bastards and Guile Heroes. (They should also know it's a snake when they bring it in.) These characters rarely, if ever, get angry, but when they do, it's usually because someone has taken advantage of their trusting nature one time too many, or has dared to hurt the ones they love. This may occasionally result in the character taking a level in badass, or revealing a hidden badass side, but this type of character is very effective at delivering An Aesop without having to resort to violence, whether it's through a Shut Up, Hannibal! speech, giving the villain his "The Reason You Suck" Speech, or asking a friend What the Hell, Hero?, though they are also just as likely to inform hero and villain that You Are Better Than You Think You Are.
Contrast Insufferable Genius and Mad Scientist. May be a Gentle Giant. When they are lucky and carefree instead of compassionate, they're The Fool. See also Idiot Hero, Dumb Is Good and Emotions vs. Stoicism (this landing on the "emotions good, logic bad" side).
In Suite Pretty Cure ♪, Hummy is a rather dense optimist who is unable to hold grudges or remember depressing events for long, allowing her former friend, Siren to take advantage of her. However, these same traits eventually help Hummy win Siren back over to the side of good.
Puella Magi Madoka Magica: the eponymous character is kind and simple, which means that she's often taken advantage of by Kyubey. It gets worse from there. And in the end, she manages to retain her kindness and Messiah ID... but only via playing a massive Gambit and ascending to goodhood.
Taipu from BIONICLE, to the point where his friend Onepu constantly takes advantage of him.
In Usagi Yojimbo, a mentally challenged man is a great friend of Kitsune. Unfortunately, he's framed for one of her crimes, and is executed for it, despite him being one of the nicest people in town. Kitsune (and other people outside the comic) was driven to tears.
Pumbaa from The Lion King. Even his name means "simpleton". Despite not being too bright, this little piggy's got a big heart of gold and is really good with lion cubs.
Bertie from Jeeves and Wooster. Most of the plots consisting of him getting himself into trouble while trying to solve his friends' problems.
Toby Kwimper in Richard Powell's Pioneers Go Home!, probably the only person in the world who could walk into a bank to get a loan, be mistaken for a robber and come out of it all with the hoped-for loan due purely to a character reference from the bank president. Toby commented in his narration that when trying to obtain money from a bank it probably helped to have either a really good character or a really bad one.
Live Action Television
Kenneth from 30 Rock, an example so famous he made the Trope Image. Although there are multiple blink-and-you-might-miss-them moments that imply that Kenneth's life might be a bit Darker and Edgier than it seems on the surface. One example that comes to mind is when he rattles off one of his family's "classic Southern recipes." One of the ingredients he lists is a Union soldier.
Kramer from Seinfeld. The only person who cares about his fellow human beings in the franchise.... and is portayed as an idiot by Larry David because of it.
Joey from Friends is a dim-witted womanizer, but an incredibly loyal and caring friend.
Nate from Gossip Girl is the dumbest of the main characters, and probably the sweetest too, especially compared to Chuck and Blair.
The Big Bang Theory: Zack Johnson, a secondary character. Unlike most of Penny's boyfriends (who are usually muscular, dumb as well as rude and obnoxious), Zack is extremely dim-witted but also an easygoing, friendly person who genuinely likes Penny's nerdy friends and makes a genuine effort to get to know them.
Noob has Sparadrap, who is both one of the dumbest and one of the nicest characters of the franchise. One of his guildmates is a Manipulative Bastard to whom he mentions lending game currency without getting it back in the comic.
Patrick, similar to his friend Spongebob, is a well-meaning idiot, and fits this trope for the most part.
Winnie the Pooh is a gluttonous idiot, but extremely gentle and friendly. Most of the supporting cast aren't far off this trope either. This is prominent in the original novels too, though most prevalent in the Disney adaptations.
The latter half of Ren and Stimpy in contrast to the smarter but manic and violent tempered Ren.
Finn from Adventure Time is the embodiment of this, as he's said to slay anything evil and will always help anyone in need. His love for being a hero can go a bit Yandere at times, but he always means well.
Peter Griffin was this on Family Guy before Flanderization sets in. While his irresponsibility caused a lot of trouble, he really did care for his family. In later seasons, he's a borderline Villain Protagonist who has killed several people.