The secondary structure of an RNA molecule plays an integral role in its maturation, regulation, and function. Over the past decades, myriad studies have revealed specific examples of structural elements that direct the expression and function of both protein-coding messenger RNAs (mRNAs) and non-coding RNAs (ncRNAs). In this work, we develop and apply a novel high-throughput, sequencing-based, structure mapping approach to study RNA secondary structure in three eukaryotic organisms. First, we assess global patterns of secondary structure across protein-coding transcripts and identify a conserved mark of strongly reduced base pairing at transcription start and stop sites, which we hypothesize helps with ribosome recruitment and function. We also find empirical evidence for reduced base pairing within microRNA (miRNA) target sites, lending further support to the notion that even mRNAs have additional selective pressures outside of their protein coding sequence. Next, we integrate our structure mapping approaches with transcriptome-wide sequencing of ribosomal RNA-depleted (RNA-seq), small (smRNA-seq), and ribosome-bound (ribo-seq) RNA populations to investigate the impact of RNA secondary structure on gene expression regulation in the model organism Arabidopsis thaliana. We find that secondary structure and mRNA abundance are strongly anti-correlated, which is likely due to the propensity for highly structured transcripts to be degraded and/or processed into smRNAs. Finally, we develop a likelihood model and Bayesian Markov chain Monte Carlo (MCMC) algorithm that utilizes the sequencing data from our structure mapping approaches to generate single-nucleotide resolution predictions of RNA secondary structure. We show that this likelihood framework resolves ambiguities that arise from the sequencing protocol and leads to significantly increased prediction accuracy. In total, our findings provide on a global scale both validation of existing hypotheses regarding RNA biology as well as new insights into the regulatory and functional consequences of RNA secondary structure. Furthermore, the development of a statistical approach to structure prediction from sequencing data offers the promise of true genome-wide determination of RNA secondary structure.