The existing answer already gives the essentials. This variation in reading Revelation 22:14 persists across quite a number of modern English translations.
I thought it might help to have a bit of explanation, too, especially if readers have some sense of the textual landscape for the NT. Not for nothing does the introduction to the Nestle-Aland edition point out that
The manuscript tradition for the Book of Revelation differs greatly from that of the other New Testament writings.1
The two textual traditions appear this way:
The image is taken from H.B. Swete's The Apocalypse of St. John... (3rd edn; Macmillan, 1911), p. 307.
The top line corresponds to the text adopted by the NIV, the bottom line is the KJV ("Majority") text version, or in the form typically seen in modern editions of the Greek NT:
[οἱ] πλύνοντες τὰς στολὰς αὐτῶν
those who wash their robes
[οἱ] ποιοῦντες τὰς ἐντολὰς αὐτοῦ
those who do his commandments
How to decide which is the original reading, though? Three considerations (at least) speak in favour of the "robes" rather than "commandments" reading (in descending order of significance):
- As noted by @fdb, the "oldest" manuscripts have this reading. The textual witnesses to the very difficult text of Revelation are fewer than in other NT books, however.2 The manuscript support for "robes" is in Sinaiticus, Alexandrinus (4th and 5th C respectively), and "about 15 minuscles", while the "commandments" reading is in the tenth C 046, most minuscles, and is reflected also in the Syriac* and Coptic tradition.
- When John of Patmos speaks about "commandments", he uses τηρεῖν "to keep" rather than ποιεῖν "to do", as the KJV version has it. If the "commandments" reading was original, this would be an odd form of the phrase.
- In the context of 22:12 ("...I am coming soon, and my reward is with me to pay each one according to what he has done!"), scribes might be inclined towards prefering a "moral" sense in v. 14.
* On the Syriac, see fdb's comment following this answer.
Cumulatively, Swete was justified in writing (see reference above) that
Upon the whole, then, πλύνοντες κτλ. ["washing etc."] may with some confidence be preferred; and it yields an admirable sense."
- Various editions of N-A have slightly different wording of this sentence (which appears in "2. The Greek Witnesses" sub "Consistently Cited Witnesses in Revelation"), but make the same point, always citing J. Schmid, Studien zur Geschichte des griechischen Apokalypse-Textes (3 vols; Munich, 1955/56). The discussion of James Moffat in the Expositor's Greek Testament (Hodder & Stoughton, 1897), vol. 5, pp. 281ff. is still well worth a read. His discussion of this precise textual point appears on p. 490, n. 2.
- This is the pay-off from the point in n. 1. See on this, Tobias Nicklas, "The Early Text of Revelation", in The Early Text of the New Testament ed. by C.E. Hill and M.J. Kruger (OUP, 2012), pp. 224-237.