I would say that of the songs I sing, I play about 90+ percent of them in the key I am singing, rather than use the transpose button ... this helps me so that if I am just singing while someone else is playing, I remember what key I sing the song in ... Of course there are exceptions, as previously mentioned, if the song is more 'comfortable' to play in a certain key ... one example of this is the beautiful Jobim song "Once I Loved" which I enjoy playing in the 'Real Book' key of Dmin (F), but sing in the key of Amin (C) ... for this song I use the transpose button ...
Any 'instrumentals' that I play are in whatever key they are written in the 'Real Book' or other fake books or music sheets ...
Like chas, I also do not like to play in the key of 'B', and would prefer to play in the key of 'Gb' rather than 'F#' even though they are the same key ... Overall I prefer the 'Flat' keys to the 'Sharp' keys ... as chas said just "a mental thing I guess" ...
One bad feature of using the transpose button - which has happened to me - is, let's say you have a style set up in the KB for a certain song and you have set the style with a -2 transpose setting ... if you are playing with another musician and call out the key as written in the music, and not the transposed key, you are definitely going to have a problem ...
As an add-on to what John C. has said above, when I was studying accordion, there was a fellow who played 'jazz accordion' in the style of the great Art Van Damme ... this guy learned every song in every key ...