I have heard hundreds of performance of this song cycle, have sung it, and have accompanied it (though having to take some shortcuts, as it is fiendishly difficult to play well). My first recording was by the Danish tenor Axel Schiótz, a recording made in the 1930s (he later suffered a stroke and had to reinvent himself as a baritone - still later he taught in Minnesota, Colorado, and Toronto). I played that record every day until I wore it out - I was ecstatic when it was remastered onto CD.
The legendary recording of the cycle, which made it well-known in Anglophone as well as German-speaking countries, was by the German baritone Dietrich Fischer-Dieskau brilliantly accompanied by the English pianist Gerald Moore. There are many other fine renditions of this song cycle, including those by Ian Partridge (tenor), Sanford Sylvan (bar.), Olaf Baer (bar.), Christopheren Nomura (bar.) and, in English, Shura Gehrman (bass) - just to mention a few in my collection.
I have now put this recording, by the English tenor Ian Bostridge, at the top of my list. I think it's simply wonderful, especially in the more lyrical songs like Der Neugierige (#6) and Tränenregen (#10). More to the point, I think it likely closest to what Schubert had in mind. In that regard, I note a reviewer calls the voice immature. I wouldn't use that word - perhaps young and innocent would be more apposite - but after all the protagonist of these songs is a love-sick young man who is sighing over a girl he can't have, an unrequited love which may push him over the brink into suicide. I guess one could call that immaturity, but it's the kind of immaturity that gave rise, beginning with Goethe's Young Werther (first published a generation before Wilhelm Müller wrote his Müllerin poems), to the Romantic movement. I think Ian Bostridge has perfectly channeled that young man in this exquisite performance.
It should be noted that Schubert did not set all of Müller's Müllerin poems. He left out five (Prologue, Epilogue and three verses), and for some reason it was decided to have Fischer-Dieskau read them between songs of this set. If this were vinyl, I would find this a serious drawback, especially as some of the poems are very long. As it's a CD, it's easy enough to skip over these readings - which I do.
Finally, the pianist, Graham Johnson (the pianist in the entire 40-CD Hyperion Schubert set, and the guiding spirit behind that project), is very fine indeed, and the sound is first-rate. Highest possible recommendation.