How many times has this theme been used? The first two that came to mind were The Iron Giant, and that more recent one where the monster looks like a gigantic Sean Penn. Now comes A Monster Calls, featuring a character who looks (to me) a bit like the tree guy from Guardians of the Galaxy.
And they just remade “Pete’s Dragon.”
There are the (very) little kids that sing to Mothra.
For every one of these, the tales of the 10,000 children EATEN by monsters are never told… 
The Neverending Story
Monsters don’t eat people – people eat people.
Sully from Monsters, Inc. might not be giant by adult standards, but he’s still a heck of a lot bigger than the little girl.
There’s the South Park episodes where Cartman befriends Cthulhu. It was really quite charming, IMHO.
Purple people.
And the South Park mention brings to mind what (parts) of the SP story arc was parodying–My Friend Totoro.
There are all those loathsome Godzilla movies and Gamera movies where little kids befriend the kaiju.
You could arguable include (although they’re not necessarilygiant monsters)
Space Children (1958)
Tobor the Great (1954)
The Invisible Boy (1957)
Dinosaurus (1960 – kid befriends a caveman AND a brontosaurus!)
and, of course, the MST3K classic
Extraterrestrial Visitors/Pod People (1983)
Also, it wasn’t kids, but you could include son of Kong (1933) and Mighty Joe Young (1949 and 1998)
One-eyed, one-horned, flying purple people.
It’s no wonder they all starved.
Gigantor the Space age robot.
The best of these will always be My Neighbour Totoro.
Although I am curious what movie the OP is referencing about the Giant Sean Penn…
I found it: BFG.
I believe he means Yongary.
Ok, little boys have bullies- (or they are bullies in a few cases). Imaginative smart kids seem more likely to get bullied. So they (as I did) dream of having a BIG friend who will take care of that nasty bully and teach him a lesson.
The Hulk, Kung-fu are also TV series that bring this out. Bullies are taught lessons when they bully the wrong guy.
“Brenda” from Rod Serling’s “Night Gallery.”
(OK, the monster wasn’t exactly a ‘giant,’ but it was a lot bigger than the kid–and just wanted a friend.)
One that I really like is The Water Horse. It’s much more recent than most mentioned so far.