Can a spell which requires concentration be maintained when you leave it behind and enter a different plane of existence?  For example, does Blink cancel Major Image?

No, it doesn’t. Which I’ve used to advantage when using a magic circle before!

Concentration is maintained as long as you do not lose consciousness, fail a concentration check, or the spell ends or is dispelled.

And additionally, nothing says that a spell (concentration or not) loses effect on moving between planes or even just fey stepping around the corner, unless the spell says otherwise.

. . . but some spells say they end if the concentrating caster moves out of range,  as with Witch Bolt.  

Quote from CardamomConundrum >>

. . . but some spells say they end if the concentrating caster moves out of range,  as with Witch Bolt.  

Just like DxJxC said:

Quote from DxJxC >>

Concentration is maintained as long as you do not lose consciousness, fail a concentration check, or the spell ends or is dispelled.