If there's one word for what I hear in Rachmaninov's melodies, it is "yearning". He does "yearning" better than anyone else, IMHO.
My personal favorite is Rachmaninov's Prelude in G# minor, but also his Concertos 2 and 3, Rhapsody on a Theme of Paganini, and his Prelude in G# Minor. Harmonically complex, contrapuntal, involving two or more voices, polyrhythmic, involving two mathematically indivisible lines at once (i.e. 2 against 3 or 3 against 4), and most important... lyrical, imitating the human voice.
He's an expressive mastermind and I always hear something new in his music.