There is a widespread myth (as far as I know it is a myth) that orthodox Jews must have marital relations through a hole in a sheet. What is the origin of this myth and does it have any actual basis in halacha?
Although this is essentially a canard, it is possible that it is based on the Yerushalmi (Y'vamos 1:1):
דרבי יוסי בן חלפתא ייבם את אשת אחיו חמש חרישות חרש וחמש נטיעות נטע ודרך סדין בעל
The P'nei Moshe commentary (ad loc., s.v. ודרך סדין בעל) appears to interpret this as meaning that there was an opening in the sheet. The essential purpose of R' Yose ben Chalafta's behavior was to minimize his pleasure and thereby demonstrate that his actions were solely for the purpose of the mitzvah of yibum, considering that his wife (or wives, as perhaps suggested by Tos. Shabbos 118b, s.v. אימא) was from a levirate marriage (ad loc., s.v. אתיא).
(The version of the story in the Bavli Shabbos 118b omits mention of a sheet and does not maintain that R' Yose was in a levirate marriage. For more on the Yerushalmi, see Maskil L'David §44 by Rabbi David Lau).
This Yerushalmi is cited by the Hagahos Maimoniyos (Hil. Issurei Bi'ah, 21:8) as an example of marital restraint in general, but the context seems to suggest that he was referring to the frequency of the act rather than the manner. (However, see the Bi'ur HaGra on Shulchan Aruch OC 240:8, s.v. ויש מפרשים, who interprets the Hagahos Maimoniyos as referring to the manner as well).
Generally speaking, physical contact is considered an essential aspect of marital relations, which is why divorce is mandated if either the husband or the wife demands that they remain clothed during relations (Shulchan Aruch EH 76:13; cf. commentaries ad loc., Magen Avraham OC 240:22). CYLOR for specifics; but, generally speaking, the old canard about the hole in the sheet is not actually practiced.
The myth derives from seeing Jews in religious neighborhoods hanging their “talitot katan” out to dry. This poncho-like garment is about two feet by four feet, has a fringe on each corner, and a hole in the center for the wearer's head, and it looks somewhat like a small sheet with a hole, and many people have vivid and warped imaginations.