nee ねー, ねえ, ねぇ

In Japanese, nee ねえ, also spelled nee ねぇ, or nee ねー, is the relaxed pronunciation of nai ない, or a longer variant of the ne ね particle, or an interjection used to call people's attention, or the word oneesan お姉さん, "older sister," without honorific affixes.

Manga: Karakai Jouzu no Takagi-san からかい上手の高木さん (Chapter 1, 消しゴム)

• 無い
• ね Particle
• Interjection
• 姉

無い

In manga, most of the time nee ねー means nai ない.

• warukunee
  悪くねえ
  (same as...)
• warukunai
  悪くない
  Not bad.

• ore janee
  俺じゃねえ
  (same as...)
• ore janai
  俺じゃない
  [It] is not me.

• shiranee
  知らねえ
  (same as...)
• shiranai
  知らない
  [I] don't know.

• shindenee
  死んでねえ
  (same as...)
• shindenai
  死んでない
  (same as...)
• shinde-inai
  死んでいない
  [He] isn't dead.
  • See: 居抜き言葉.

• un ga nee
  運が無え
  (same as...)
• un ga nai
  運が無い
  [I] don't have luck.
  • See: double subject constructions.

Manga: Gintama 銀魂 (Chapter 28)

• onna wo nameru-n-janeeeee!!
  女をなめるんじゃねェェェェ！！
  Don't underestimate women!!

As a matter of fact, nai ない isn't the only word that can end up being pronounced with ee ええ instead. Many i-adjectives can end up being pronounced this way.

For example, sugoi すごい, "amazing," is often pronounced as sugee すげえ, hayai 速い, "fast," as hayee 早え.

Manga: Boku no Hero Academia, 僕のヒーローアカデミア (Chapter 1)

• Context: All Might punched a villain so hard it started raining. (seriously.)
• migite ippon de
  tenki ga kawacchimatta!!!
  右手一本で　天気が変わっちまった！！！
  He changed the weather with just his right arm!!!
  • Literally:
    With one right arm the weather ended up changed!!!
  • ippon 一本
    One cylindrical object. (one arm, in this case.)
• sugeeeeee
  すげぇぇぇぇぇ
  AWESOOOOOOME
• kore ga...
  Ooru Maito!!!
  これが…オールマイト！！！
  This [is]... All Might!!!

ね Particle

Sometimes, nee ねえ is a longer form of the ne ね particle, which is generally used to seek agreement.

Manga: Assassination Classroom, Ansatsu Kyoushitsu 暗殺教室 (Chapter 1, 暗殺の時間)

• Context: a tentacle monster destroys the moon and will destroy the Earth next year unless his class of assassin students manage to kill him before then.
• koroseru to ii desu nee
  殺せるといいですねぇ
  If able to kill: good, right?
  It would be good if [you] could [manage to] kill me, don't you agree?
• sotsugyou made ni
  卒業までに
  Until graduation. (i.e. within one year.)
  • See also: dislocation.

Interjection

Sometimes, the nee ねえ particle is used as an interjection, to call someone's attention.

Manga: Karakai Jouzu no Takagi-san からかい上手の高木さん (Chapter 1, 消しゴム)

• Context: Takagi 高木 catches Nishikata 西片 acting suspiciously.
• nee, Nishikata.
  ねえ、西方。
  Hey, Nishikata.
• na, nani!? Takagi-san!?
  な、何？！高木さん！？
  W-what [is it]?! Takagi!?
• nani shite-n-no?
  何してんの？
  What are [you] doing?
• betsuni... nanimo...
  別に･･･何も･･･
  Nothing... in particular...
• fuun.
  ふーん。
  *suspicious humming of doubt.*

姉

Sometimes, nee 姉 means oneesan お姉さん, "older sister." Similarly, nii 兄 would be oniisan お兄さん, "older brother."