This paper presents a general-purpose, wide-coverage, probabilistic sentence generator based on dependency n-gram models. This is particularly interesting as many semantic or abstract syntactic input specifications for sentence realisation can be represented as labelled bi-lexical dependencies or typed predicate-argument structures. Our generation method captures the mapping between semantic representations and surface forms by linearising a set of dependencies directly, rather than via the application of grammar rules as in more traditional chart-style or unification-based generators. In contrast to conventional n-gram language models over surface word forms, we exploit structural information and various linguistic features inherent in the dependency representations to constrain the generation space and improve the generation quality. A series of experiments shows that dependency-based n-gram models generalise well to different languages (English and Chinese) and representations (LFG and CoNLL). Compared with state-of-the-art generation systems, our general-purpose sentence realiser is highly competitive with the added advantages of being simple, fast, robust and accurate.