One of my favorite things about the new Star Trek movie is the callbacks to previous films and episodes. All are done in a subtle way, not in the George Lucas way.
Star Trek VI: the Klingon blood globules are emulated by the way the red matter appears.
Star Trek V: thankfully nothing
Star Trek IV: The Romulan Wessles joke is remembered when Checkov tries to work the intercraft, also Spock giving Scotty a formula that he invented in another timeline.
Star Trek III/VI/Generations: Kirk often finds himself hanging off a cliff.
Star Trek II: the Kobayaski Maru, and Kirk's eating an apple.
Star Trek I: Admiral Pike's uniform
The Cage: Pike's wheelchair
Where No Man: a planet named Delta Vega
Also I liked seeing Admiral James Komack.