Many non-coding RNAs with known functions are structurally conserved: their intramolecular secondary and tertiary interactions are maintained across evolutionary time. Consequently, the presence of conserved structure in multiple sequence alignments can be used to identify candidate functional non-coding RNAs. Here, we present a bioinformatics method that couples iterative homology search with covariation analysis to assess whether a genomic region has evidence of conserved RNA structure. We used this method to examine all unannotated regions of five well-studied fungal genomes (Saccharomyces cerevisiae, Candida albicans, Neurospora crassa, Aspergillus fumigatus, and Schizosaccharomyces pombe). We identified 17 novel structurally conserved non-coding RNA candidates, which include four H/ACA box small nucleolar RNAs, four intergenic RNAs and nine RNA structures located within the introns and untranslated regions (UTRs) of mRNAs. For the two structures in the 3' UTRs of the metabolic genes GLY1 and MET13, we performed experiments that provide evidence against them being eukaryotic riboswitches.