The characters in Independence Day are all individuals, and extremely well played by the actors. This extends to minor characters like the children, and some very small cameo roles that add so much to this movie like the very small role of Captain Jimmy Wilder played by Harry Connick, Jr. Some of my favorite moments are played by minor characters. There are so many memorable appearances and lines in Independence Day, it is impossible to list them all.
Here is one conversation between Will Smith and Jeff Goldblum that shows the mixture of humor and action that you see throughout the movie:
David Levinson: We're hit! We took a hit!
Captain Steven Hiller: [yelling] We're not hit! We're not hit! Stop side-seat driving! \
David Levinson: [trying to make a break for the exit] Left! Left! Tunnel! Tunnel! Exit! Exit! Left!
Captain Steven Hiller: Where the hell do you think I'm going?
David Levinson: Ok, ok We're we're we're uh...
David Levinson: Uh oh they're closing up on us... they're closing...
Captain Steven Hiller: Shut up, shut up, shut up!
David Levinson: Must go faster. Must go faster! Must go faster! Go, go, go, go!
Captain Steven Hiller: [escapes from the alien ship] [screaming]
Captain Steven Hiller: Aaaaaaahhhhhhhhh!
Captain Steven Hiller: Oh! Elvis has left the building!
David Levinson: Oh, thank you very much. Oh, I love you man!
Many of the lines from Independence Day have entered our general American culture, so much so that we don't even notice. Just as an example, I accused my 14 year old daughter of sideseat driving earlier today.