I've never been much of a New World fan, though I appreciate how Williams lifted the "duh duh.... duh duh...." for Jaws from it. He went somewhere else with it, but stole two of the most memorable chords in music. Jaws, and "Satisfaction" are the only two songs I can think of that a typical person can identify by 2 notes. If a new listener heard that part of New World, they'd immediately think of Jaws.
Instead, I'll offer up some more Dvorak. Op. 22 Serenade for Strings in Eb Major - I link to 2 things because the "crappy commercial" one plays a part near the beginning of the piece, and the next link is a later but complete movement. It'll give a good sense for what it has to offer.
first part
later movement
Here's another nomination, and please excuse the stupid video that comes along with it. This is the most "known" part of the piece, so it's a good link for that purpose.
Saint Saens Symphony No. 3
And everyone knows
Canon in D by Pachelbel. Start listening around 1:45 of that link to hear where the recognizable part of it begins. Or, well, listen to the whole thing. I doubt that this is new to anyone, though. Even the new guitar versions are good (search for JerryC or funtwo if you don't know what I'm talking about).