Tokyo Mew Mew: "Mew" is both a homophone of "mu" (a Greek letter and biological term, fitting with the Little Bit Beastly cast) and an onomatopoeia for a cat (the main character is a Catgirl).
Yakitate!! Japan refers to the main character's signature "Japan" baked goods. ("Pan" means "bread" in both Japanese and Spanish.)
The title was adapted into Portuguese as Amassando Ja-pão, which not only keeps the pun, but does so in a single language.
Gintama; the word on its own means "silver soul" and revolves around the main character Gintoki, but is a near homophone for the word "kintama" which means "testicles".
The title of Urusei Yatsura literally translates to "People from the Planet Uru", although the word "Urusei" (which comes from "urusai", meaning annoying) is also a Japanese colloquialism to tell someone to "shut up" and the title can be interpreted as "Hey guys, shut up!" Animeigo attempted to translate the pun by changing the title to Those Obnoxious Aliens for the short-lived English dub of the anime. Of course, the main character is Moroboshi Ataru, whose name literally means "hit by a falling star", so the title is only the beginning of the Hurricane of Puns.
The episode titles in Strawberry Marshmallow, at least in English, vary between rhymes, alliteration, and this. For examples of this: "Violent Night", "The Hat's Meow", "Attack of the Killer [ZZZs]", "Into Hot Water", "Sick Jokes", "The Matsuri" (a borderline example: a matsuri is a festival as well as the name of a main character), "Schooled", and "Heart Attacks". Parts of the "An Amusing Stew (Using Miu)" episodes have titles as well: "Lack of Acute Judgment", "Thumb War", "Thrown By the Goat", "Phony", "What Possesses Her", and "Sketchy".
The Street Fighter video games had a TV anime series titled Street Fighter II V (that's a roman numeral "two" and the letter "vee"). The title doesn't seem to mean much by itself at first, but "two vee" is pronounced almost similarly to "tee vee", as in a Street Fighter TV series. The "V" also stands for "Victory" and since "two" can be a homophone for "to", the title can also be read as Street Fighter To Victory.
Dub episodes are often a pun on the featured Pokémon, such as "To Master the Onix-pected" and "Turning Over a Nuzleaf".
Pokémon 3: Spell of the Unown refers to two things: 1) the fact that Unown are Pokémon based on the alphabet, and 2) their powers.
Other episodes still have punny titles without Pokémon names, like "Gotta Catch Ya Later!" (a pun on the franchise's early Catch Phrase), "Hoenn Alone" (using the name of the home region of the Advanced Generation arc - this is the first episode of said arc, even), or "Home is Where the Start Is" (one of the arc-transition episodes when Ash returns to Pallet Town, this one bridges the gap between AG and the Diamond and Pearl).
Done away with as of Best Wishes, which goes back to the style of the early episodes.
The American episodes sometimes go to "gems" such as "Doin' What Comes Natu-rally" and "Smells Like Team Spirit". Japan sometimes fall to this ("Do Coil Dream of Electric Mice!?")
Haré+Guu: its original title, "Janguru wa Itsumo Hare Nochi Guu", is usually translated as "The Jungle was always nice, then came Guu" (or "Haré always lived in the jungle, then came Guu" - the title uses the name of both main characters to make the pun). However, the last three words are regularly used in Japanese weather forecast, and can be interpreted as something like "clear with a chance of showers". Thus, the title's underlying meaning would be "The jungle is always clear with a chance of showers."
A.I. Love You: "ai" is the Japanese word for "love," it is pronounced like the letter I, and the second letter being "I" just completes the phrase "I love you", as well as referring to Artificial Intelligence.
A rather ironic example is Girls und Panzer. The Japanese pronunciation of "panzer" is "panzu", while the word "panties" is pronounced as "pantsu", as Lampshaded in some of the show's trailers. The irony comes in the fact that this show has no panty shots at all (despite the presence of other forms of Fanservice).
Koufuku Graffiti: The Japanese word for "happiness" and "appetite" happened to be pronounced the same way, as "Koufuku"note These two words are Chinese loans; and in different forms of Chinese they still sound relatively similar. The Japanese written title actually has one kanji taken from the two words to make the point across. There's a good reason why Studio Shaft's animated adaptation prefers using this Untranslated Title rather than the manga's own Gourmet Girl Graffiti; it's a series where Food Porn and Orgasmically Delicious appears Once an Episode.
Kill la Kill manages to pack a surprisingly large number of puns in its title. 'Kiru', depending on how it's written in Japanese, can mean 'to wear (clothes)' (着る), 'to cut' (切る), 'to kill a person' (斬る) and, of course, the English word 'kill' (キル), all of which are good for describing the show. The OST follows suit by having most tracks be named for weird variants on the show's title in a Hurricane of Puns that often makes very little sense to those who can't speak Japanese.
The franchise's Japanese title, "Purikyua", (プリキュア) is a pun on the word "Purikura" (プリクラ), which are photo booths which take pictures in Japan.
PriPara, despite the name being a shortened version of "Prism Paradise", uses this same pun. It Makes Sense in Context, since the arcade machine upon which it is based takes your picture each time you play and has a purikura mode.
"Shima" means both "striped" and "island", which could refer to two things: the stripes on Shimajiro himself or the island he lives on.
The titular character's name, Shimajiro, is a pun on the phrase "shimasho" or "Let's do it!". This does make sense, seeing as the show is based on the Kodomo Challenge program, which teaches preschoolers how to accomplish important life skills.
The Onegai My Melody movie is titled "Onegai My Melody Yuu and Ai". While this can be translated to "Please, My Melody: Friendship and Love", the pun comes in how the kanji are supposed to sound like the English phrase "You and I".