Deep learning-based approaches to protein structure prediction, such as AlphaFold2 and RoseTTAFold, can now define many protein structures with atomic-level accuracy. The AlphaFold Protein Structure Database (AFDB) contains a predicted structure for nearly every protein in the human proteome, including proteins that have intrinsically disordered regions (IDRs), which do not adopt a stable structure and rapidly interconvert between conformations. Although it is generally assumed that IDRs have very low AlphaFold2 confidence scores that reflect low-confidence structural predictions, we show here that AlphaFold2 assigns confident structures to nearly 15% of human IDRs. The amino-acid sequences of IDRs with high-confidence structures do not show significant similarity to the Protein Data Bank; instead, these IDR sequences exhibit a higher degree of positional amino-acid sequence conservation and are more enriched in charged and hydrophobic residues than IDRs with low-confidence structures. We compared the AlphaFold2 predictions to experimental NMR data for a subset of IDRs known to fold under specific conditions, finding that AlphaFold2 tends to capture the folded state structure. We note, however, that these AlphaFold2 predictions cannot detect functionally relevant structural plasticity within IDRs and cannot offer an ensemble representation of IDRs. Nevertheless, AlphaFold2 assigns high-confidence scores to about 60% of a set of 350 IDRs that have been reported to conditionally fold, suggesting that AlphaFold2 has learned to identify conditionally folded IDRs, which is unexpected, since IDRs were minimally represented in the training data. Leveraging this ability to discover IDRs that conditionally fold, we find that up to 80% of IDRs in archaea and bacteria are predicted to conditionally fold, but less than 20% of eukaryotic IDRs. Our results suggest that a large majority of IDRs in the proteomes of human and other eukaryotes would be expected to function in the absence of conditional folding.