The LEGO Movie frequently (though not completely) parodies summer blockbuster movies. The fact that Everything's Built with LEGO helps, as even the most spectacular explosions and overloaded action sequences end up sillier as a result.
Singin' in the Rain, considered one of the all-time great film musicals was itself intended as an affectionate parody of the original big Hollywood musicals. Right down to there being an overblown fantasy sequence inside the overblown fantasy sequence.
The Carry On film series were one of the first films that did parodies. In many cases, it was because the production team wanted to make a friendly rival between films that they were parodying and see what made more in the British box office.
This Is Spinal Tap is a fairly obvious example of this, it being a parody of the hard rock and Heavy Metal of the 70s and 80s. It's shown to be an affectionate parody by the sympathetic portrayal of the band towards the end of the film, and the fact that it references things that only fans of the genre could possibly get.
Christopher Guest, who played Nigel Tufnel in the movie This Is Spinal Tap, has gone on to make several mockumentaries of his own, such as Best in Show (dog shows), Waiting for Guffman (local theater) and A Mighty Wind (1960's folk music), all of which can be considered affectionate towards their (rather daft) characters.
Stephen Chow's All for the Winner was a parody of Chow Yun-Fat's God of Gamblers, but it was so well-received (by some reports even out-earning the original) it was tied into the series "officially" with two more sequels starring Chow and several other movies without him.
Airplane! is an Affectionate Parody of disaster movies, especially the movie Zero Hour! (with which it shared entire lines of dialogue, such as "The life of everyone on board depends upon just one thing: finding someone back there who can not only fly this plane, but who didn't have fish for dinner"), and one of the best Deconstructions you'll ever see. It's now very, very hard to play the "disaster on a plane" trope straight— and impossible to watch Zero Hour! or read the Arthur Hailey book Airplane is based on (it's from the guy who wrote Airport) without going into hysterics from visualizing all the jokes in Airplane!
Mel Brooks is a Grand Master of this trope. He has made it clear that he only parodies movies and genres he likes. In fact Mel Brooks has said that he could never do a parody of, for instance, slasher flicks because he can only work with genres he respects.
Young Frankenstein is an Affectionate Parody of the 30's Universal Frankenstein movies. It is so well done in that style that it is possible to miss that it was a parody. Points to the director for recreating the way the films from back in the day were made; gigantic, multi-story sets (like the lab, that managed to all fit onto screen, with its huge staircase), extended takes done without cuts, as well as just the slow and deliberate way the actors move and talk.
Blazing Saddles is an affectionate parody of Westerns, so affectionate that the singer of the theme song, Frankie Laine, did not know it was a parody. They added the whip sounds into the music later.
The Fifth Element can be seen as straight Science Fiction flick, but works very well as a friendly parody of common action and science fiction concepts, particularly those of European sci-fi/fantasy comics.
My Name Is Nobody takes this concept to its logical extreme, no wonder as it was produced by Sergio Leone himself. Whimsical, hysterical, warm and ultimately an achingly gentle farewell to the genre he himself created, it's a wonderful mood-rollercoaster of satire and homage, to the point you will cry Manly Tears every bit as much as laugh while watching it.
Enchanted was Disney's Affectionate Parody of... itself, replete with Shout Outs and and subverted tropes. Not that it didn't turn out to still be a good film (which it did).
Slither is an affectionate parody of (roughly Seventies-Eighties era) horror movies.
Grease was an Affectionate Parody of 1950s teen musicals, although most people don't seem to realize this.
Cry-Baby was an Affectionate Parody of teen musical, and they made sure everyone would realize it.
Samurai Fiction affectionately parodies traditional samurai epics while including a few modern art-film touches — and a rock-and-roll soundtrack supplied by co-star Tomoyasu Hotei.
Music and Lyrics is an Affectionate Parody of "disposable" bubblegum pop music, and its slightly pretentious-yet-cheesy tendencies, from the 1980s — especially in the mock MTV video clip for fictional band Po P!'s big hit "Pop! Goes My Heart" — to the present day, with the Britney / Christina Aguilera-type pop star character.
Snakes on a Plane is an affectionate sendup of a number of genres, such as airplane disaster, animal horror, and even action-adventure.
The Fearless Vampire Killers, or, Pardon Me, But Your Teeth Are In My Neck is a parody of the Hammer Horror vampire films that were so popular when it was made, and it works so well that it's sometimes more suspenseful than they are. This was in itself later adapted into the stage musical Tanz Der Vampire, which includes songs mimicking various musical styles.
The Turkish move GORA parodies, well, pretty much every big-budget Hollywood sci-fi movie ever made. At the beginning, the extraterrestrials are talking in English before realizing what they're doing and switching into Turkish. The prisoners on the alien ship carry lightsaber shivs. Even the main character Arif is very conscious about doing things 'right', including finding an appropriate hero costume and having his sidekicks film him as he embarks on his adventure.
Tremors, while not an out-and-out parody, includes several gentle swipes at 50's monster-movie plots.
Eight Legged Freaks was an affectionate parody of monster B movies. Had the nice blend of features like the characters playing their roles without any obvious irony, the classic trope of toxic waste causing spiders to mutate, and it even had spiders acting cartoony and making cartoony noises, and yet everything was played straight.
Die Hard started as both an action film and an affectionate parody of 80s action films, notably in casting Bruce Willis, who was best known before Die Hard for comedy roles. The movie ended up becoming the template for future action movies and transformed Willis into an action star. And the Die Hard movies eventually became an Affectionate Parody of themselves.
Hot Fuzz self consciously uses every possible cop movie trope it can, often hanging a lampshade on them, while paying tribute to those films.
Austin Powers and The Second Best Secret Agent in the World are affectionate parodies of the James Bond style of spy movies. Which were heavily inspired by Our Man Flint. Ausin lampshades this, saying In Like Flint is his favorite movie.
Hobgoblins was clearly meant to be such a parody of Gremlins — an incredibly stupid idea considering that Gremlins is itself a parody, of both the "monster attacks small American town" genre of horror films and the "A Boy and His X" genre of feel-good family films.
Stanley Donen's sadly all-but-forgotten 1978 film Movie Movie was a loving Valentine to the cheesy B-list 1930s/early '40s era black-and-white films Hollywood would churn out during the height of the old studio system. Complete with lines so cornball they'd make Captain America blush. It's glorious fun for fans of vintage kitsch.
Vampires Suck parodies Twilight. Given who's parodying it, affectionate is probably not the right word though.
Super Junior's film, "Attack on the Pin-Up Boys" is an Affectionate Parody of the idolculture, obsessions with passing fads, and the life of a teenager set in a High School A.U.. The second half of the film dips into Deconstructive Parody territory though as it becomes more introspective than the first half.
Woody Allen has parodied genres like 1970s sci-fi (Sleeper) and epic historical romances (Love and Death). One section of Everything You Always Wanted to Know About Sex* but were afraid to ask parodies 1960s Italian films, and another 1940s-50s mad scientist films (complete with John Carradine as the scientist in question).
Casa De Mi Padre is an affectionate parody of telenovelas and grindhouse movies.
Sky High is fond of pointing out the more ridiculous tropes in both the superhero and high school drama genres, which it typically accomplishes by using them straight but to an absurdly over-the-top degree. For example, the Commander has an entire drawer full of identical phones for when he pushes the buttons too hard.
Back to the Beach is a parody of 1960's Annette Funicello / Frankie Avalon beach movies, starring...Annette Funicello & Frankie Avalon!
Vamps is one for nearly every vampire movie ever made.
Lemonade Joe, or Horse Opera is an Affectionate Parody of The Western pulp movies, and quite the Cliché Storm. There are no Western movies made by Czechoslovakian film school, just this one, and you can sense just how much everybody involved in the movie loved it to bits.
Rock Slyde is a parody of Film Noir, even having the first scene in black & white, though doesn't last.
The short The Your Name Here Story is a parody of corporate promotional films. It is intentionally vague on what exactly it is about or who makes it, and thus is supposed to be "all purpose". The product is referred to as "Your Product Here" so it can fit any number of inventions and the company is also just "Your Product Here". The product is described as astounding to ridiculous manners. It apparently helps training your dog, lets you have more spare time, helps shave your facial hair, grow better crops, helps your cigarette taste better, help keeps your romance alive, helps you lose weight, and helps various other things.