These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: The Prince of Tennis
Base Breaker: Ryoma, Atobe, Horio, and to a lesser extreme Sakuno.
Creator's Pet: Echizen, but only in the manga since he's quite more sympathetic in the anime.
Several characters, but specifically: Sakuno (Ryoma/anyone shippers, but Momo/Ryo and Tzu/Ryo fans are specially bad), Yukimura (Atobe/Sanada fans) and Yanagi (Inui/Kaidoh fans). To a milder degree Momoshiro (Inu/Kai too), Kawamura and Saeki (Tezu/Fuji for both).
An doesn't have it THAT bad, but she still gets pot shots for "stringing Kamio along" and "playing with his feelings." Which brings up rather creepy Unfortunate Implications about how women should "owe" men love because they show open interest on them. (or for that matter, anyone owing anybody else love in such circumstances.)
Ryoma is very frequently accused of being one of these by his anti-fans. When a 12 year old boy is already a 4 time tennis champ (in the US) it's kinda hard not to see it. But still, lots of the accusations come from rabid Atobe and/or Rikkaidai fans... who then go and make themMary Sues and try to pass them as Better Than Canon.
Other character who have been given the God-Mode Sue ball at one point or another are Yukimura, Fuji, Tezuka, Sanada, Atobe and Kevin Smith from the anime.
Launcher of a Thousand Ships: ...Who has NOT been paired up with either Keigo Atobe, Tezuka Kunimitsu and Shuusuke Fuji in fanfiction and doujinshi, people? Sakuno also verges on the trope, since she's often used as a Possession Sue by some fangirls.
Also Ryoma, naturally due to being the main character and by far the prominent shota of the series.
Misaimed Fandom: Fan Dumb. An Tachibana's actions during the Senbatsu arc were not supposed to be seen as "awesome" and "proper of a strong female character". They were supposed to be a part of An Aesop in regards to how seeking violent resolution to a conflict is not worth it. Specially considering that Kirihara could have died after that Staircase Tumble—and that almost everyone blamed Kamio for the incident! And that An herself broke down crying in regret when Ryoma unmasked her and Kamio called her out!
Moe: Sakuno and Tomoka, specially during the Jyousei Shounan anime arc.
One True Threesome: The fandom likes the idea of building an infamous OT5 between Atobe, Fuji, Ryoma, Sanada and Tezuka to avoid Ship-to-Ship Combat. There's also the Rikkai Troica variant where Sanada hooks up with both Yanagi and Yukimura...
Rikkai fans have been whining for several years about how the team was portrayed in the anime and about The Switch between Yagyuu and Niou not being featured in their match. Lots of fans of the manga often say it of the original after the Hyoutei arc (the anime had caught up to the manga, changes started to be made).
Subverted later, when the OVA's start covering the Nationals arc and get praise for portraying some rather... polemic manga scenes in a much more understandable and sympathetic light. I.e., Ryoma cutting Atobe's hair when he's still almost unconscious in the manga is switched to Ryoma having second thoughts about it, Taki offering to have his own cut hair instead to spare Atobe the humiliation... and then Atobe swiping Ryoma's razor and willingly cutting his own hair. Or the rendition of the Rikkai matches, which also include flashbacks of the Rikkai regulars anxiously waiting for Yukimura in the hospital, remarking on their True Companions bond.