Poincare invariance of Dirichlet and Neumann boundary conditions
The Dirichlet boundary condition, in particular, breaks spacetime translation invariance. This is reflected in the string spectrum, that is, a Goldstone boson state appears in the massless spectrum of the string. This state corresponds to the collective coordinate which parametrizes small oscillations of the Dirichlet 'brane' or D-brane on which the string is constrained to move on.
For the SUPER-string, a similar effect occurs whereby a Goldstino state appears in the massless spectrum, and this indicates the breaking of some amount of spacetime supersymmetry by the D-brane.
References: String Theory, Polchinski, Volume I (equation (8.6.18) and pages 268-269), Volume II (pages 138-140).