Lexical databases following the wordnet paradigm capture information about words, word senses, and their relationships. A large number of existing tools and datasets are based on the original WordNet, so extending the landscape of resources aligned with WordNet leads to great potential for interoperability and to substantial synergies. Wordnets are being compiled for a considerable number of languages, however most have yet to reach a comparable level of coverage. We propose a method for automatically producing such resources for new languages based on WordNet, and analyse the implications of this approach both from a linguistic perspective as well as by considering natural language processing tasks. Our approach takes advantage of the original WordNet in conjunction with translation dictionaries. A small set of training associations is used to learn a statistical model for predicting associations between terms and senses. The associations are represented using a variety of scores that take into account structural properties as well as semantic relatedness and corpus frequency information. Although the resulting wordnets are imperfect in terms of their quality and coverage of language-specific phenomena, we show that they constitute a cheap and suitable alternative for many applications, both for monolingual tasks as well as for cross-lingual interoperability. Apart from analysing the resources directly, we conducted tests on semantic relatedness assessment and cross-lingual text classification with very promising results.