WordNet sense 1 (successive (without a break)):

consecutive

WordNet sense 2 (having the ends united so as to form a continuous whole):

endless

WordNet sense 3 (`continual' (meaning seemingly uninterrupted) is often used interchangeably with `continuous' (meaning without interruption)):

continual

WordNet sense 4 (uninterrupted in time and indefinitely long continuing):

constant, perpetual, unceasing

WordNet sense 5 (continuing in time or space without interruption):

uninterrupted