Like many other pianists, I use the Henle edition for studying the Beethoven sonatas, as well as a lot of other piano music. It is expensive, but you get what you pay for: notes are invariably well laid out on the page, and you can be fairly confident that all the important sources (especially the autograph – where available – and first editions) have been consulted and analyzed by editors who know their business. Conrad Hansen’s fingerings are inspired; like no other edition of piano music known to me, they force the player to phrase correctly, without demanding that you also be a contortionist. Henle is also unusual because minor revisions are added silently in new printings of the same edition. This admittedly can result in some confusion unless you check the publishing history carefully, but if you buy a recent copy instead of xeroxing your library's older one you will be assured of getting the latest version.
On occasions where differences between sources exist, the choice of which to use is sometimes obvious, but on other occasions, it is anything but. Henle’s editor, Bertha Wallner, generally makes good calls, but it is always best to decide for oneself. At the very end of the Appassionata, in m.352, for instance, the first and third eight-notes in the bass clef are F’s in the first edition, whose printing Beethoven presumably oversaw. However, clearly marked in the autograph are A-flats. Wallner thinks that was an error, and she may well be correct. But perhaps not. Playing the A-flats allows the extra punch of a renewed F in the next measure where the cascading arpeggiated chords are written double forte.
I always play through Schnabel's edition once (but only once), and only after I have thoroughly learned the sonata. He offers fascinating and provocative interpretive advice, but he certainly was dogmatic, and often just states his opinion without supporting it with any argument. Especially annoying is his refusal to condone even the slightest adjustments Beethoven would have had to make in order to counter the limited range of whatever piano he had at hand. I have no problem extending the bass a note or two when it seems obvious that Beethoven needed, say, a contra E that was not available to him, as in m.2 of the second movement of the Waldstein, but I invariably observe any variation he composed in order to get around the limitations imposed by his lack of treble notes. Another Schnabel curiosity is the system of Roman numerals he employed to indicate measure numbers within a phrase. Thinking deeply about such issues is of utmost importance, of course, but his system of counting measures often seems arbitrary.
I also keep a copy of the Tovey-Craxton edition close by, for one reason only: Donald Tovey's pithy comments that precede each sonata. Unlike his book on the sonatas that now seems pedantic and old-fashioned, his remarks to the performer are chock-full of advice that is witty and wise in equal measure. He would have been a lot more fun to argue with than Schnabel. He may even have listened to what I had to say.
Von Bulow's comments in the Schirmer edition give insight into the thinking of a great musical mind of the 19th century, but his edition, like the Schnabel, who at least made a strong effort to deliver an accurate text, should serve solely as a reference, not something to learn a work from. Copious editorial suggestions that we constantly see in front of us, no matter how perceptive, have a way of affecting our interpretation in spite of our best intentions to avoid their influence. Why do you think politicians keep on repeating the same lies time and time again?
Not being a theorist I do not prostrate myself on the floor whenever the name Schenker is uttered, even though I freely recognize his invaluable contribution to our comprehension of tonal music. His credentials aside, however, I have never felt drawn to his edition of the Sonatas. I own a copy but seldom find it helpful in comparison to any of the others I have mentioned.
All the above editions are what today's students would call old to ancient. Others exist, and new ones appear now and then. However I have not examined them and so I leave it to others to comment upon them, or compare them to those editions that have served my generation extremely well.