Experiments in atomic, molecular, and optical (AMO) physics rely on lasers at many different wavelengths and with varying requirements on spectral linewidth, power, and intensity stability. Vertical external-cavity surface-emitting lasers (VECSELs), when combined with nonlinear frequency conversion, can potentially replace many of the laser systems currently in use. Here we present and characterize VEC-SEL systems that can perform all laser-based tasks for quantum information processing experiments with trapped magnesium ions. For photoionization of neutral magnesium, 570.6 nm light is generated with an intracavity frequency-doubled VECSEL containing a lithium triborate (LBO) crystal for second harmonic generation. External frequency doubling produces 285.3 nm light for resonant interaction with the 1 S 0 ↔ 1 P 1 transition of neutral Mg. Using an externally frequency-quadrupled VECSEL, we implement Doppler cooling of 25 Mg + on the 279.6 nm 2 S 1/2 ↔ 2 P 3/2 cycling transition, repumping on the 280.4 nm 2 S 1/2 ↔ 2 P 1/2 transition, coherent state manipulation, and resolved sideband cooling close to the motional ground state. Our systems serve as prototypes for applications in AMO requiring single-frequency, power-scalable laser sources at multiple wavelengths.