Likewise, Ouran High School Host Club has fun with parodying a lot of cliches associated with romance and high school comedies, even though the series itself falls under both banners (and the manga artist herself had written things like it in the past until Ouran became her breakout hit).
The anime has somewhat different characterizations and cuts off with a Gecko Ending, but it still manages to be both a hilarious reverse harem parody and gender farce and a high-quality reverse harem series in its own right.
Although Neon Genesis Evangelion is meant to be a deconstruction of Giant Robot series, the creators are such big fans of the genre that they cannot help but show affection to some of the genre tropes.
Despite its successor becoming one of the most influential and popular anime franchises in history, the original Codename: Sailor V manga reads like a lighthearted parody of the Magical Girl and Henshin Hero genres. While Sailor Moon could be pretty jokey at times, it doesn't come close to matching the sheer absurdity of Sailor V.
The first Ganbare Goemon OVA sees Goemon and Ebisumaru race to rescue Omitsu from a castle, while being thrown into spoof levels of Grandia, Castlevania and Twinbee.
Project A-Ko was a sendup of just about everything in anime between 1976 and 1986.
One Piece is a fairly standard Shōnen anime with a focus on humor that occasionally leans toward parody. The most obvious, though, is cowardly hero Usopp's disguise of "Sogeking", a clear parody of live-action tokusatsu series'. He even has a theme song, complete with 60's style Japanese Live-action special effects and the appearance of being largely filmed inside a quarry.
The 2008 Dragon Ball OVA is almost an Affectionate Parody in its own right. A lot of its humor is derived from Lampshading various absurd aspects of the series' tropes.
Big O is a parody of a number of manga/comics/anime subsets...Batman, Mazinga Z, Astro Boy, Cutie Honey, Lupin III, and the 80's anime OVA "A Wind Called Amnesia"...not to mention Phillip Marlow/Sam Spade detectives.
Macross was originally going to be a sendup of the mecha anime genre, back in the day when a city-sized spacecraft shifting to robot mode was considered ridiculous. However, it proved so popular that the creators wound up playing it straight to a much greater degree... and thus setting up a whole new generation of parodies!
The show itself could be seen as poking fun at Unwanted Harem setups; it uses a similar setup of one guy surrounded by girls, except for the facts that 1. it's dead obvious from early on that the First Girl Wins and 2. all the involved characters are various degrees of insane and the series focuses far more on their antics than it does on any relationship aside from the obvious winner.