Depending on the instrument, guitar or piano, I do tend towards the same.
on piano, as mentioned, I'll play different voicings of chords so I don't have to venture (too) far off the white keys. C Dm Em F G Am. That said, I have many songs that start in Am to C, Em to G etc
on guitar, I like to use open chord voicings so I tend to ring out the high E and or B string in many chords. One example I use alot is an Am chord tabbed out like this:
-0-
-0-
-5-
-7-
-0-
-x-