Epistle of Barnabas. If this book was truly by the companion of Paul, then there might be reason to consider it for the canon. But there is insufficient proof of this, and its late date (c. 90-130) makes it unlikely to have been written by Barnabas [MacD.FormCB, 146]. It also makes use of numerology.
Shephard of Hermas. Reading this book, which Von Campenhausen describes as "more jejune and superficial than the Johannine Revelation," [VonCamp.FCB, 216] brought to mind another book - Bunyan's Pilgrim's Progress. It is, like that work, self-evidently allegorical, and perhaps indeed inspired; but it was obviously written too late (2nd century) to be attributed to the Apostles.
Paul's Epistle to the Laodiceans. Metzger notes that this work was finally, once-and-for-all excluded from the canon in the mid-1400s. Now of course it should be easy to see why this work hung around for as long as it did: if it truly is a work of Paul, then it meets the criteria of apostolic authority and deserves to be considered for the canon. But there is nothing to assuredly connect it to Paul, and even if there were, it is in content "almost entirely a compiliation of extracts from the Pauline Epistles." [Black.Marc, 61] In other words, without Laodecians, we ain't missin' nothin' anyway!
1 Clement (also consider 2 Clement). It comes as no surprise that the works of Clement (or works allegedly by him - 2 Clement's authenticity is questionable) were considered by some as worthwhile, for he was a disciple of Peter. Hence, under the criterion of apostolic authority, his works could have entered the canon under the same principles as Luke and Mark did, but he is disqualified by other criteria. In particular, 1 Clement refers to a phoenix as an actual living creature!
Preaching of Peter. Although recognized (by ONE PERSON that we know of!), a late date makes this document unlikely to have been written by Peter.
Apocalypse of Peter. Same as the above. This work was written around 125-50 AD [Metzg.NT, 184], too late for Peter. It bears a haunting resemblance to works like Dante's Inferno, and thus may be inspired in the same category as the Shepherd.
Gospel According to the Egyptians. This work was written around 150 AD (ibid., 169) and was accepted as canonical only in Egypt (naturally). It appears to have been written to promote the doctrines of the Encratites.
Gospel According to the Hebrews. We have no current translation of this work (ibid., 169) so we cannot evaluate it, other than to say that it was probably written in the middle of the second century.