Dere comes from Japanese word “deredere” (デレデレ) which usually means "Lovestruck". It is a typification given to Anime/Manga chacters (sometimes used in real life too) as a form of reflection to their character traits. There are more than 10 "Dere" Types in anime but I will just discuss the most popular one.
1. Tsundere
Tsundere is probably the most popular or mostly used "dere" In anime and manga. From its word "tsun" Itself comes from the Japanese word “tsuntsun” (ツンツン) which means to be aloof or high and mighty.
They are stucked between their pride and love that makes them miserable at expressing their own feelings towards the person that they love. They are easily embarrassed or didn't know what to do with their affection that mostly results in violence. You can easily distinguish if the character is tsundere or not because they mostly used the phrase "It's not that I like you or anything." to the person they care about.
Tsunderes might be egoistic and violence at the outside but they are more loving and caring at the inside. They just don't know how to express their feelings.
Popular Tsunderes:
Chitoge Kirisaki (Nisekoi)
Erina Nakiri (Food Wars!)
Taiga Aisaka (Toradora!)
Tohsaka Rin (Fate/Stay Night)
2. Dandere
This one is the opposite of Tsundere although they are both bad at confessing their feelings. The word "dan" comes from the Japanese word “danmari” (黙り) which means silence. They are known for their shy, quiet and antisocial behaviors.
Despite of their behavior, they are actually sweet and caring persons. They actually want to be friendly and talk to other people but they are scared and easily embarrassed. They are afraid to say something that may upset or make people awkward so they choose to stay quiet.
But of course if you've become friends with danderes, their attitude might change and you'll find them rather cheerfull and cute persons.
Popular Danderes:
Nagisa Furukawa (Clannad)
Sawako Kuronuma (Kimi Ni Todoke)
Hinata Hyuuga (Naruto)
Kosaki Onodera (Nisekoi!)
Nadeko Sengoku (Bakemonogatari)
3. Kuudere
The word Kuudere comes from the Japanese pronunciation of the word "Cool"(クール) which means Calm and Composed. They never panic over any circumstances. Its hard to find them being happy, excited, surprised, scared, sad, annoyed or getting angry. You can identify them as an emotionless people.
Most of the Kuudere are called Geniuses, Talented and Exceptional. They are maintaining their image thats why its hard for them to show weakness and emotions. When it comes to personal affection, it is hard for them to express their feelings and some didn't know what exactly feelings mean.
Its really difficult to fall in love to Kuuderes but for me falling for them is the most romantic in anime. It is thrilling to find what side of them they might show especially their smiles.
Popular Kuuderes:
Kanade Tachibana (Angel Beats!)
Origami Tobiichi (Date A Live)
Saber (Fate/stay night)
Mikasa Ackerman (Attack on Titan)
Mei Misaki (Another)
Shiina Mashiro (Sakura-sou no Pet na Kanojo)
4. Yandere
The "yan" in Yandere comes from the Japanese word “yanderu” (病んでる) which means to be sick (in this case mentally sick). These type of character will probably you'll never find attracting. Although they are normal at the outside, like a normal socially sweet and caring person, they becomes crazy because of love.
Yanderes mostly resorts to violence when it comes to the love. They even do murder just to stop someone from taking away their loved ones (mostly their rivals in love). You may find them as Angels outside, they are actually a monster inside. And its very common in seinen or some shounen animes because it is unique and refreshing plot for an anime.
Popular Yanderes:
Satou (Happy Sugar Life)
Kaede Fuyou (Shuffle)
Anna Nishikinomiya (Shimoneta)
Megumi Shimizu (Shiki)
Lucy (Elfen Lied)
Yuno Gasai (Future Diary)
I hope you'll like it. I will make Part 2 of This Discussing other Unpopular Type of "Deres"
very nice read. enjoyed and especially it touched me in different way as i relate alot thanks