It touches the earlier films, plot-wise, granted...but quite tenuously enough. I would never think I was watching the same movie twice. They're all part of one big story which, if you look hard enough, have great paralels with human experience.
Taking a step back from themes and the like, I thought the film was beautiful

I was immensely touched by 'Up', but I didn't cry. However, I grew up with Toy Story (I was 4 or 5 when the first one came out), and Toy Story 2 was the last ever film I saw in my local cinema before it was closed down because the building had to be condemned. After campaigning and restoration, it was reopened last year and Toy Story 3 is the first film I've seen there. Kinda fitting!
Anyway, crying...yes, I did. I welled up at the incinerator scene, and I had tears filling my glasses up during Andy's farewell. I'm proud to say so, too, because it means the animators did their job fantastically. I mean, how do these guys do it?! I was more moved by several plastic-y CGI characters than by any human actor! Maybe its because real faces have lives away from the camera which (especially if they're famous faces) take you further away from the film's heart, so to speak. Woody and Buzz's faces were made for Toy Story only, and that helps a lot!