Do a search for 'Greek Apostolic Fathers Online' and you will be directed to a blog entry by Stephen Carlson that directs you to the CCEL website, which claims to present Kirsopp Lake's public domain edition. Alan Humm's jewishchristianlit.com points to the same thing.
Unfortunately, it has become apparent in our 1 Clement Greek Reading Group that the CCEL text of 1 Clement, at least, is riddled with errors, including egregious misspellings and the omission of large verse sections.
Here are some alternatives (1 Clement only):
(1) Saint Clement of Rome (dabar.org; HT: earlychristianwritings.com) (only 1 chapter at a time)
(2) Κλήμεντος Προς Κορινθίους Α (only chapters 1-22)
(3) Rico's Apostolic Father's Lookup (only 1 chapter at a time...why is that??)
(4) early church texts (links to Rico's Lookup; only displays one chapter at a time)
Option 2 will work fine until we pass chapter 22. The restriction to one chapter viewing in options 1, 3-4 is annoying. Why is it that no one seems to make the whole text available at once?
Update: (5) At DocumentaCatholicaOmnia, the whole text of 1 Clement can be downloaded as a PDF, and copied from there as unicode text. The best option yet! HT: Ken Penner.