All the members tropes have been moved to the Character page.
Tropes in general
Adorkable: They may be serious as the grave one moment and a bunch of goofballs the next.
Those who have been featured on We Got Married tend to show this side, especially Leeteuk, who becomes the epitome of this in the show. Despite being the eldest he has no idea how to react to his pretty new wife. Same case with Donghae, who was not actually "married" on the show but was featured with an actress. It was so bad that he had to be helped before and during their dates.
Aerith and Bob: Eeteuk, Heechul, Han Geng, Yesung, Kangin, Shindong, Sungmin, Eunhyuk, Siwon, Donghae, Ryeowook, Kibum, Kyuhyun, Zhou Mi, and Henry. While Han Geng and Zhou Mi's names are obviously not Korean, Henry's just sticks out.
They made many appearances in other artists' videos. Kibum was in The Grace's "My Everything", Siwon was in Girls' Generation's "Hoot", Sungmin acted in Dong Bang Shin Ki's Banjun drama episode as Yoochun's childhood friend, and so on.
By the other hand, some of their MVs had guests: Yoona was in "U" and "Marry U" (before SNSD's debut), Jessica was in "Super Girl", Sunny was in "Cooking Cooking" and Fx's Victoria was in Suju-M's "U" before f(x) made their debut.
Cats Are Mean: Heechul's cat, Hanjayheebum — or Heebum for short. Also, his original cat hated everyone but him.
Genre Roulette: The core group's six albums so far cover bubblegum pop, ballads of all sorts, contemporary R&B, electropop/synthpop, and an example of their label's own unique style, SMP, which mixes pop, rock and orchestral music. There's also a song on their sixth album that sounds a bit like the lovechild of trot and dubstep.
Gratuitous English: On their show 'Full House'. It used to be more prevalent in their raps, but seems to be on the decline...
Korean Drama: Several of them have played roles in different dramas. Most popular perhaps is Rainbow Romance, which featured six of the boys in its last season (although only Kibum and Heechul were members of the main cast).
Subverted as these are all stage names given by their company.
Meganekko: Eeteuk in particular used to wear lensless glasses. Several of the others have done this as well; Zhou Mi seems particularly fond of them. Yesung's family business, Y Style, has been advertised by the boys on Twitter through pictures of them as Meganekkos.
Name's the Same: Yesung's real name can either be spelt "Kim Jongwoon or "Kim Jongun." Unfortunately, the current dictator of North Korea is also named "Kim Jongun". In 2009, a Swedish tabloid erroneously used Yesung's photo in an article about the then-heir apparent to Kim Jongil and the jokes about it still haven't completely died down.
There's a Korean comedian also called Lee Hyukjae, Eunhyuk's real name. They made a joke out of it when the two were on the same variety show once, by jokingly snubbing the comedian and pretending all queries towards him are meant for Eunhyuk.
No Export for You: This is pretty much the condition of any place that is not East or Southeast Asia, Australia, or California.
Older Than They Look: Most of the boys haven't physically aged since their debut in 2005. Especially Leeteuk and Heechul who are almost 30.
One of Us: Aside from the fact that some members are techies and gamers (most notably Kyuhyun), there's their love for Disney and Eunhyuk's interest in manga, particularly One Piece. Also, there's the occasional reference to 9GAG and memes.
Pet the Dog: When their Chinese member Hankyung was insulted with racist remarks by people outside of their dorms, Heechul and several of the others went out to beat the guys up.
An incident in December 2011 during which SM Entertainment's mistreatment of them affected their fans as well pushed some of the boys too far, leading to a series of outbursts on Twitter—including religious, gentlemanly Siwon.
Rummage Sale Reject: Pretty much everybody in the fifth album concept photos, with Eeteuk being one of the worst.
Schedule Fanatic: But as one of the top idol groups in South Korea, they don't really have a choice.
Serenade Your Lover: Where lover = TV wife, with Leeteuk (a) calling his We Got Married partner Kang Sora up on stage during his "She" number in Super Show 4 for a "proposal", and (b) allegedly writing a love song for her in their sixth album. Meanwhile, lover = fandom in Super Junior classics "Marry U" and "From U".
Stepford Smiler: Leeteuk (one of the more cheerful, upbeat and talkative members) is an extreme case of Type A. When asked about his life with his parents as a child, Leeteuk revealed while crying that not only was their relationship bad, but they abused him often to the point where he began hating and being afraid of his own father — yet for the most part, he continues to smile. It's very sad and eerie to watch.
He also used to run a club for depressed idols, to back this up a little.
All of Super Junior and even most idols could be considered a watered down case of this too. Depression is very common within the Kpop scene, although Leeteuk does seem to be a very worrying example of it being a reality.
Word is that she's accepted, but there's no marriage date set yet. (Shindong has actually asked people to stop asking him about it.)
Leeteuk dragged his "wife" Kang Sora on-stage to propose at a concert, serenading her while handing her a rose then presenting the ring. Which turned out to be too big. So he hugged her to make up for it.
Attack Backfire: Turns out the attacks with shit bags made the targets even more popular than before, and that's the reason Siwon, Heechul and Kangin are trying to get attacked as well.
After Donghae discovers this and confronts Kibum, he expresses how annoying it turned when the attack backfired, so for the last attack, they make Donghae popular. Donghae later states being famous is annoying as well.