Played with in Fate/hollow ataraxia when the cast gets drunk and then adds animal tics to their speech such as nya! (cat) or wan (dog) based on what their favorite animal is.
In Fate/stay night itself, Saber has a particular way of pronouncing Shirou's name (she puts the emphasis on the wrong syllable) that is subtle enough that many English speakers don't pick up on it, but in-story is said to be very distinctive.
Moran in Shikkoku No Sharnoth often answers statements or questions with either 'Yes. No.' or 'No. Yes.' followed by an explanation.
Misuzu Kamio in AIR, who is fascinated with dinosaurs, often says "Gao" (her idea of the sound a dinosaur makes) when surprised, distressed or embarrassed.
Gao is the sound a dinosaur makes in Japanese. (For extra credit, look up the Japanese word for a dog's barking.)
Kanon is full of such characters: Nayuki ("nyuu"), Makoto ("auu"), and Ayu ("uguu"), to the point of being overdone. It adds tremendously to the moe factor of the girls though, especially in Ayu's case - it's just so darn cute, which it is also helped by the marvelous performance of Yui Horie, Ayu's voice actress.
Though not a heroine, Sayuri Kurata from Kanon tends to say "ho-e?" in addition to her more usual "ahaha." Whether or not this is influenced by Sakura from Cardcaptor Sakura is unclear; although, due to Sakura's Genki Girl personality, her ho-es are usually much more verbal.
Nagisa Furukawa is fond of ending her sentences with desu~.
Also used for a Deconstruction which is then Played for Laughs: Tomoya suggests that Sunohara says 'and a toilet seat cover' at the end of every sentences. Sunohara did so, but in the end, frustratedly complain that it's ruining every of serious sentences he's saying.
Kotomi Ichinose has a habit of ending her sentences with "-no".
Little Busters! has 'wafu~' for Kud, which she uses all the time, and 'fuee' for Komari, mostly as an expression of surprise.
Rena Ryuuguu has a habit of repeating the final words of sentences, most famously kana, kana (I wonder, I wonder). More to the point, "kana kana" is supposed to be the sound higurashi cicada make.
Satoko Hojo has a habit of speaking with over-formal grammar and ending her sentences with wa, giving the impression she's trying very very hard to sound like The Ojou. She also uses "nii nii" to refer to her older brother, which sounds childish, but is also the name of a different kind of cicada.
Rika Furude likes to use nipaa~ (an onomatopoeia for 'smiling') and mii (a kitten meowing, translated in the English release of the manga as "mew"). Technically, not onomatopoeia but phenomime. Rika also has a habit of saying "nano desu" after her sentences, which is translated as "Sir" in the official manga translation (she uses sir for everyone, including her friends, no matter their gender).
Hanyuu's trademark is a cry of au au au! when she is upset.
In the second episode of Higurashi Kira, Fairy Hanyuu ends most of her sentences by saying her own name.
In Umineko: When They Cry, Maria has her trademark "Uu~." This actually has some significance to the plot. One day she forgot the words to a song, so she replaced the words with an "uu-" sound. It made her mother smile, so from that point on Maria believed that saying "uu-" was a spell for happiness. It's also something of a deconstruction; if her mother is to be believed, the weird speech pattern is one of the reasons why she's bullied in school and has no friends. It's certainly the reason said mother smacks her because she finds it irritating.
In the English translation of the visual novels, Dlanor A. Knox always puts emphasis on the last word of every SENTENCE. Which is written in UPPERCASE. The Japanese version has her end her sentences in copulas written in katakana.
Spark Brushel is a reporter who likes to ends most phrases with "End Quote", End Quote.
Det. Gumshoe ends most of his sentences with "Pal" when he's addressing someone, Pal. In the Japanese version he slurs the end of his sentences. He doesn't like it when someone tries to copy his verbal tic:
Zeppy, being a little squid and all that, is unable to say anything other than "Kwui-kwui."
The resident god wannabe, Iris, has a habit of singing as she talks, indicated by the eighth note (♪) placed at the end of her sentences.
In the Perpetual Testing Initiative of Portal 2, it turns out one alternate universe Cave Johnson is an extremely nice guy who randomly says "Chariots" at the end of his sentences. This is much to the annoyance of Cave Prime, who had chosen that word as the sign that you're talking to him and not any alternate Caves.
In Katawa Shoujo, Misha loves to add "Wahaha~" to the ends of her sentences. And her beginnings. For that matter, she'll just randomly say it.
Hagakure ends a few of his sentences with "-be". This has been translated by the thread as "'right" (which is as close to the connotations of "be" in a Tohoku dialect that one can get with a single English word). Monobear/Monokuma's "upupupu" could possibly also count as one, to a lesser extent.
In the official English localization, Hagakure's tic is translated as "for serious".
In Virtue's Last Reward, Sigma has a rather unusual tic of "talking like a cat whenever talking about cats". This results in a good number of cat puns, and a number of interesting reactions from the other characters.
Sigma: Oh that? It's a book meow-ht cats.
Alice: A...meow-ht, cats?
Sigma: Oh, sorry. It's a sorta...tic I've had since I was a kid. Can't help talking like a cat when talking meow-ht cats.
On the same page, "Zero Jr.", an A.I rabbit, has a tic that he speaks in rabbit puns.
Zero Jr: All you need to know is that anybunny who tries to sneak out gets hit with a biiiig penalty.