Although it is generally assumed that there are two dominant classes of gamma-ray bursts (GRBs) with different typical durations, it has been difficult to classify GRBs unambiguously as short or long from summary properties such as duration, spectral hardness, and spectral lag. Recent work used t-distributed stochastic neighborhood embedding (t-SNE), a machine-learning algorithm for dimensionality reduction, to classify all Swift GRBs as short or long. Here, the method is expanded, using two algorithms, t-SNE and UMAP, to produce embeddings that are used to provide a classification for 1911 BATSE bursts, 1321 Swift bursts, and 2294 Fermi bursts for which both spectra and metadata are available. Although the embeddings appear to produce a clear separation of each catalog into short and long bursts, a resampling-based approach is used to show that a small fraction of bursts cannot be robustly classified. Further, three of the 304 bursts observed by both Swift and Fermi have robust but conflicting classifications. A likely interpretation is that in addition to the two predominant classes of GRBs, there are additional, uncommon types of bursts which may require multiwavelength observations in order to separate them from more typical short and long GRBs.