When C. R. Gregory published his revised list of New Testament manuscripts, it included only the four manuscript categories we know now: Papyri, Uncials, Minuscules, Lectionaries. In the updated 1923 list of E. von Dobschütz, however, a new category -- Talismans -- appeared. Von Dobschütz's 1933 list added still another category, Ostraca.
Ostraca are, of course, potsherds. New Testament ostraca are potsherds of vessels which had once had New Testament verses written on them.
Talismans are amulets or other decorations containing small passages of scripture. A typical talisman contained a copy of the Lord's Prayer and was worn around the neck.
By the time of von Dobschütz's 1933 list, nine talismans and twenty-five ostraca were cataloged. The talismans were designated by a gothic T (𝕿) with a superscript (i.e. 𝕿1...𝕿9) while the ostraca were designated by a gothic O (𝕺) with superscript (𝕺1...𝕺25).
The talismans generally cannot be cited in New Testament editions; how does one tell if a copy of the Lord's Prayer is supposed the Matthean or Lukan form? (𝕿3 has, however, been cited for Matthew 6, as it contains the final doxology found only in Matthew's version. Interestingly, however, it has only a partial form of this doxology.)
When Kurt Aland took over the catalog and published the Kurzgefasste Liste, he abolished the two little-used categories. The most important talisman, 𝕿1, became 0152. The primary ostraca (𝕺1-𝕺20, a collection of sherds from the same seventh century pot) became 0153. (It contains parts of the four gospels, with no part more than about thirty verses long; three hands are believed to have been involved). However, neither 0152 nor 0153 is cited in any major modern edition (they are not mentioned in NA27, UBS4, the current editions of the harmonies, or in the pocket editions of Merk and Bover). In effect, the talismans and ostraca have been discarded for textual criticism.
Old Testament scholars are still willing to admit them, it seems. An ostracon in New York's Metropolitan Museum of Art has the Rahlfs number 841 and contains parts of 1 Esdras 9:21-24. It is cited in Hanhart's Göttingen edition of that book.
I will admit that I wish more of these items were still in the lists, although I'm not concerned with whether they are numbered as talismans or simply as uncials or whatnot. (In this I agree with J. Keith Elliott, who also believes these other categories of witnesses should be re-admitted.) 𝕿2, for instance, is quite interesting. It is Muhlenberg College (Allentown, Pennsylvania) Theological Papyrus 2, or Oxyrhynchus Papyrus 1077, an amulet from the sixth century containing Matthew 4:23-24 "in mystical forms." Even if it doesn't tell us much about the New Testament text, it is surely worth studying for historical reasons!
We might note that, even if these classes of items were restored to the critical editions, it might not cover all possible classes of evidence. There are also mosaics and murals -- and even dirty floors! I don't know of any New Testament texts preserved in a floor, but at the palace of Aï Khanum, there is a section of the floor which preserves an extensive text in reverse. It is believed that a papyrus text was copied, then dropped on the floor while still rather wet, and the text off-printed onto the clay floor. If the photo in Peter Green's Alexander to Actium: The Historical Evolution of the Hellenistic Age (p. 109) is to be believed, the text proved surprisingly legible.
Drawings in manuscripts can also have textual value. Many illuminated gospels have drawings of the four evangelists writing their gospels (or sometimes we see an illustration of a scribe copying a manuscript). These drawings will show the text -- sometimes twice (the original, or the divinely inspired text, and the copy). This artwork can contain text. There aren't many big variants in the first few words of Matthew, Luke, or John, but the sixth and seventh words of the usual text of Mark are ΥΙΟΥ ΘΕΟΥ. UBS3 placed these words in brackets; they are absent in א* Θ 28 etc. The words are found, e.g., in the text of Mark shown in Pierpont Morgan Library MS. 692 (ℓ1635), folio 123v. Possibly -- very likely -- the text in the illustration is taken from the text of the manuscript. But the issue must be examined.