"Would also like to hear what other people would consider Mahler's favorite works?"
You have to keep in mind that it wasn't until late in Mahler's career that he got to conduct much symphonic repertoire. The majority of his conducting work was in opera. Among operas, the late Du Ponte operas of Mozart; Don Giovanni; Tales of Hoffmann; Die Freischutz and Fidelio would be obvious candidates. He also liked Lehar operettas, but wouldn't admit to it during formal discussions or heated debates. Mahler was crazy about R. Strauss' "Salome", but never got to conduct it because of the court censors in Vienna. He and Alma walked out on "Elektra" in New York, and I very much share that view as well.
In regards to symphonic stuff, obviously the Beethoven symphonies; Beethoven piano concertos; late Mozart symphonies; Schubert 9; the four Schumann symphonies (which he loved); late Haydn symphonies and Haydn's "Creation" (which I believe he conducted twice). As someone has already mentioned, "Symphonie Fantasique" was an obvious influence, and Mahler conducted it on more than several occasions. I do believe that Mahler got around to all four Brahms symphonies, but he conducted the Third the most. At some point, he did voice his preference for Brahms 3 (which makes sense to me). Oddly enough, Mahler did not conduct much Bruckner.
Mahler did his own version of Bruckner 4, which I've been told has several severe cuts to it (Rozhdestvensky has made a difficult-to-find recording of it). Mahler gave one of the earlier performances of Bruckner 6. To my ears, the beginning of the scherzo to Bruckner 6 sounds very similar to the very beginning of Mahler 6 (repetitive low A in the double basses). Also, the sort of 'telegraph rhythm' that happens in the first movement of B6 shows up in the first movement of M7. Mahler also did Bruckner 5, but I don't know if he put cuts in it or used the Schalk edition. To the best of my knowledge, Mahler didn't conduct the last three symphonies of Bruckner.
Much to my astonishment, Mahler did not conduct the late symphonic poems of Dvorak with the singular exception of "The Wild Dove", which contains a sort of typical Mahlerian funeral procession within it. He did conduct several of the shorter orchestral works of Smetana, but I do not believe that he ever gave the entire "Ma Vlast" (someone please correct me if I'm wrong about that). Mahler very much liked the Smetana operas. At that time, I believe that Smetana was still better known in Austro/German circles than Dvorak.
In his late New York period, Mahler suddenly became far more 'continental', modern and 'catholic' (varied) with his tastes in symphonic music. He gave premieres - or certainly American premieres - of various wild and interesting works by American, British, French and Italian composers (and probably a few other nationalities as well). It's been said that when Mahler died, he possessed the score to Charles Ives' 3rd symphony. I've never found any written literature to support that claim, but it's a widely circulated story.
Going back to Berlioz, Mahler did conduct "The Damnation of Faust" and voiced his liking of it as well. "Le Troyens" would have hardly been performed at this point.
Prophetically enough, the very last item (or maybe the next to the last item) that Mahler ever conducted was the "Berceuse Elogique" by F. Busoni. It's a soft and melancholic work that appropriately ends with a solo stroke on the tam-tam.