Looking up...
映画を見る。
I will watch a movie.
To perceive with the eyes; to look at.
窓から富士山が見える。
Mount Fuji can be seen from the window.
テレビを見ながらご飯を食べる。
I eat while watching TV.
Used for both intentional looking (e.g., watching TV) and unintentional visual perception (e.g., seeing a mountain).
To watch (e.g., a movie, game, or event).
昨日の試合を見た?
Did you watch yesterday's game?
Often used with entertainment or events.
To judge, consider, or evaluate (often with a mental action).
彼の意見を見る限り、賛成だ。
Judging from his opinion, he agrees.
Implies forming an opinion based on observation.
To experience or undergo (e.g., a situation).
彼は多くの困難を見てきた。
He has experienced many hardships.
Often used in a broader, experiential sense.
見る often implies active watching (e.g., 映画を見る 'watch a movie'), while 見える is passive (e.g., 見える 'can be seen').
見る must take a direct object (e.g., 本を見る 'read a book', 景色を見る 'look at the scenery').
From Old Japanese *mi- (to see), from Proto-Japonic *mi- (to see, to look). Related to 見える (to be visible), 見せる (to show), and 観る (to watch).
見る is a transitive verb and requires a direct object (e.g., 映画を見る 'watch a movie'). For intransitive 'to be visible,' use 見える. In formal contexts, ご覧になる (honorific) or 拝見する (humble) may be used.