People worldwide use language in subtle and complex ways to express emotions. Although emotion recognition--an umbrella term for several NLP tasks--impacts various applications within NLP and beyond, most work in this area has focused on high-resource languages. This has led to significant disparities in research efforts and proposed solutions, particularly for under-resourced languages, which often lack high-quality annotated datasets. In this paper, we present BRIGHTER--a collection of multi-labeled, emotion-annotated datasets in 28 different languages and across several domains. BRIGHTER primarily covers low-resource languages from Africa, Asia, Eastern Europe, and Latin America, with instances labeled by fluent speakers. We highlight the challenges related to the data collection and annotation processes, and then report experimental results for monolingual and crosslingual multi-label emotion identification, as well as emotion intensity recognition. We analyse the variability in performance across languages and text domains, both with and without the use of LLMs, and show that the BRIGHTER datasets represent a meaningful step towards addressing the gap in text-based emotion recognition.