Greek and English:
Fowler, Harold N., W. R. M. Lamb, R. G. Bury, and Paul Shorey, trans. Plato. 12 vols. LCL. London: Heinemann, 1914–1942.
Statesman, Philebus, Ion (not openly available online)
Lysis, Symposium, Gorgias (not openly available online)
Cratylus, Parmenides, Greater Hippias, Lesser Hippias (not openly available online)
Timaeus, Critias, Cleitophon, Menexenus, Epistles (not openly available online)
Note: As always, see the Digital Loeb Classical Library for up-to-date texts and indexing, particularly for the Republic, which has a new edition translated by Christopher Emlyn-Jones and William Preddy (2013).
Burnet, John, ed. Platonis Opera. 5 vols. OCT. Oxford: Clarendon, 1900–1907.