There have been several excellent responses to Joseph Sowa's post, so I'll
just add two cents.  For a lover of the romantics, a good place to start is
the minor-mode works, where the emotion tends to be closer to the surface:

Symphony No. 40 in g, K. 550
String Quintet in g, K. 516
Piano Concerto No. 20 in d, K. 466
Piano Concerto No. 24 in c, K. 491
Piano Quartet in g, K. 478
Piano Sonata in c, K. 457
String Quartet No. 15 in d, K. 421
Serenade for Winds in c, K. 388

There are also a number of late major mode works in which Mozart evokes a
wide range of emotions. A short list might include:

Divertimento for String Trio in E flat, K. 563
Piano Concerto in No. 27 in B flat, K. 595
String Quartet No. 23 in F, K. 590
Piano Sonata in F, K. 533/494
Clarinet Concerto in A, K. 622 (especially the slow movement)

Also don't miss the Sinfonia Concertante for Violin and Viola, K.  364,
maybe his single most beautiful work.

Mozart is at his very best in opera; I'd start with Don Giovanni (the first
and last scenes are unmatched) and then go to Le Nozze Di Figaro, which is
a triumph from the first bar to the last.

Best,

Peter Goldstein
Juniata College
Huntingdon, PA