We present a systematic study on multilingual and cross-lingual intent detection from spoken data. The study leverages a new resource put forth in this work, termed MInDS-14, a first training and evaluation resource for the intent detection task with spoken data. It covers 14 intents extracted from a commercial system in the e-banking domain, associated with spoken examples in 14 diverse language varieties. Our key results indicate that combining machine translation models with state-of-the-art multilingual sentence encoders (e.g., LaBSE) can yield strong intent detectors in the majority of target languages covered in MInDS-14, and offer comparative analyses across different axes: e.g., zero-shot versus few-shot learning, translation direction, and impact of speech recognition. We see this work as an important step towards more inclusive development and evaluation of multilingual intent detectors from spoken data, in a much wider spectrum of languages compared to prior work.