To be sure, the Hammerklavier Sonata has been (and, presumably always shall be) my absolute and undisputed favorite. The reasons for this are as follows.
In movement 1, Beethoven's employment of the triple-themed exposition is arguably more effective than in any other sonata (though some may argue it was used better in Schubert's Sonata in Bb -- I however disagree on this matter), and the whole movement is a momentous tour de force. From the heralding opening chords, to the wandering and highly original development [which somehow ends up in B major (!)] to the thundering chords that conclude the movement, this movement declares the beginning of a new Beethoven -- a Beethoven that has reemerged after a little while of abstaining from composing.
In movement 2, Beethoven's Scherzo is a rare example of humor -- the only other comparable example of such raw humor is in Sonata No. 31 -- Mov. 2.
The movement 3 is a piece of pure anguish, beautiful modal harmonies, motivic development, etherealness, and unusual length. The transfiguration of 2 measures into an elaborate 30 second passage (from exposition to recapitulation) is truly remarkable. Rather than try to describe this movement in my own words, I find it better to quote the following passage from Bekker, Paul (1925). Beethoven. J.M. Dent & Sons, Ltd. p. 134, and simply leave my thoughts on the movement to be summarized by this moving quote.
"the apotheosis of pain, of that deep sorrow for which there is no remedy, and which finds expression not in passionate outpourings, but in the immeasurable stillness of utter woe".
The movement 4 is arguably the best contrapuntal work for piano ever written. Let it be known that Bach is my favorite composer, and my favorite "fugist" -- however -- I consider this fugue by Beethoven to be better than Bach's fugues. This statement alone is absolute heresy, and I am shocked that I myself am saying it. However, it is indubitably the truth, and this fugue of gargantuan proportions "con alcune licenze" is the best contrapuntal piece ever written, in my opinion.
Among some truly remarkable features of the fugue are the following:
1) that it makes extensive use of tenth leaps and trills, e.g. when the fugue begins
2) descending chromatic motif, this being the source of much of this tension and dissonance
3) the treatment of a fugue as such a raging, furious, and emotional entity, rather than treating it as an intellectual and academic endeavor, like Bach did. Examples: "augmentation of the fugue theme and countersubject in a sforzando marcato at bars 96-117, the massive stretto of the tenth leap and trill which follows, a contemplative episode beginning at bar 152 featuring the subject in retrograde, leading to an exploration of the theme in inversion at bar 209." [Willi Apel, "Retrograde," Harvard Dictionary of Music (Cambridge, Harvard University Press, 1969), p. 728.]
4) the "cantus firmus first heard at m. 250, and eventually appearing against the subject, countersubject, and respective inversions in the second-to-last episode" [this is original research found on
https://en.wikipedia.org/wiki/Piano_Sonata_No._29_(Beethoven)].
For these reasons, and simply for the gargantuan conception of the sonata as whole -- with a triple-themed exposition, third movement of incredible length, and fourth movement of gargantuan proportions -- this piece, along with the Ballade No. 4 and Goldberg Variations, are my favorite pieces for solo piano ever written.
I hope I have been of assistance.