Sex is a universal human desire, right? Actually, that's not true. Some people - and some anime characters - just don't want to have the desire. These celibate anime characters aren't looking for physical intimacy, and what's more, they don't want to be.
Celibacy isn't the same thing as asexuality. While there is some crossover between the two, asexual people simply don't experience the desire for a physical connection, but they can still experience an emotional attraction. Meanwhile, celibate people have chosen not to pursue intercourse for reasons that range from simply not having time to religious objections - they often still experience sexual attraction. Since most characters don't actually come out and say where they fall one way or the other, some of this is based on speculation. Also, some characters are shown only rejecting advances from interested individuals - it might be a completely different situation if they ever had another opportunity. So, while Shota Aizawa is on this list, it's entirely possible that he'd react differently to a come-on by someone who wasn't Miss Joke.
Most of the characters on this list are male anime characters - that's because female characters are less likely to display obvious sexual desire, so it's harder to make assumptions about what they want. There are some exceptions to this, like Mayaya from Princess Jellyfish - she's far more interested in reading about her favorite period in history than she is in getting laid.
Subaru Mikazuki - 'My Roommate Is A Cat'
Subaru Mikazuki is a mystery writer who doesn't want to interact with other people unless it's absolutely necessary. It's not just that he has social anxiety - though he probably does - it's that he actively enjoys being alone and loathes the idea of interacting with others. Currently, his biggest social struggle involves interacting with and understanding a stray cat he adopted, so he definitely hasn't reached the point where he'd be willing to let another human being come that close.
He's making big strides toward being willing and able to talk to other people, but that won't necessarily include anything beyond - and right now, it definitely doesn't.
Whether or not L actually wants to be physically intimate is up for debate - but because of his lifestyle, he's probably functionally celibate. L has been working around the clock as a detective since he was 8 years old. Spending your entire adolescence on an isolating and dangerous career is likely to squash any budding desire. While he occasionally displays attraction to Misa, this is likely fabricated to get a reaction out of Light.
In fact, the creators behind Death Note originally considered making L a father - Mello and Near being his children - but they nixed the idea on the grounds that L having children wasn't especially plausible.
Eiichiro Oda once claimed that everyone in One Piece is "in love with adventure." This was his explanation for why few of the characters have any romantic inclinations whatsoever. As the main character, Luffy is probably the best example of this concept. Luffy was unaffected when Hancock used her Love-Love Fruit, which harnesses the victim's physical desires to turn them into stone.
This implies that physical intimacy isn't something Luffy cares about. With his pirating lifestyle and effusive personality, he probably wouldn't have much trouble finding a willing partner, but it's just not on his radar.
Saiki Kusuo - 'The Disastrous Life of Saiki K.'
The only thing that Saiki Kusuo wants out of life is for everyone to leave him alone. Due to his incredible, almost unlimited powers, he has far more people paying attention to him than he can tolerate. He manages to avoid all traps set for him by Chiyo, a girl with a massive crush on him, and never reacts to Kokomi's attempts to get him to appreciate her beauty.
Maybe if he meets someone who he can relate to even a little bit, he'll change his mind, but for now his immeasurable power makes it hard for him to meet other people on their level, and he'd rather just be left alone.