Two rateless code constructions are developed for efficient communication over multi-input multi-output (MIMO) Gaussian channels. The key ingredients in both architectures are layering, dithering, and repetition. Both employ successive cancellation decoding along with minimum mean-square error (MMSE) combining and convert the MIMO channel into a scalar channel to which classical Gaussian base codes can be applied. The first construction based on simple layering induces an additive white Gaussian noise (AWGN) scalar channel and with perfect base codes achieves a substantial efficiency gain over a baseline repetition scheme. At typical spectral efficiencies, this scheme can achieve better than 85% of capacity for a rateless construction with two effective rates. The second construction which uses a diagonal layering (DL) structure is capacity achieving at any SNR and induces a particular time-varying scalar channel. This holds even if the MIMO channel is block constant but time-varying.