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We propose a new concept of rateless auto-encoders (RL-AEs) that enable a flexible latent dimensionality, which can be seamlessly adjusted for varying distortion and dimensionality requirements. In the proposed RL-AEs, instead of a deterministic bottleneck architecture, we use an over-complete representation that is stochastically regularized with weighted dropouts, in a manner analogous to sparse AE (SAE). Unlike SAEs, our RL-AEs employ monotonically increasing dropout rates across the latent representation nodes such that the latent variables become sorted by importance like in principal component analysis (PCA). This is motivated by the rateless property of conventional PCA, where the least important principal components can be discarded to realize variable rate dimensionality reduction that gracefully degrades the distortion. In contrast, since the latent variables of conventional AEs are equally important for data reconstruction, they cannot be simply discarded to further reduce the dimensionality after the AE model is trained. Our proposed stochastic bottleneck framework enables seamless rate adaptation with high reconstruction performance, without requiring predetermined latent dimensionality at training. We experimentally demonstrate that the proposed RL-AEs can achieve variable dimensionality reduction while achieving low distortion compared to conventional AEs.