Hanging a Shir LaMaalot at the Home of a New Mother and in the Hospital
It is customary to hang a Shir LaMaalot [Psalm 121]  in the room of the new mother and the newborn, immediately upon the expectant mother’s arrival at the hospital - in many cases a small laminated copy of the prayer is clipped to the baby's bassinet and/or pram.  This serves as a safeguard for the mother etc., both during the birth itself so that it will proceed normally and easily,  and also during the following days, so that they will survive for a long life. 
Another reason given is that this is a part of [the child’s] education so that the first thing that the child sees will be something holy (from this we may also infer how important it is to ensure that the child does not look at pictures of unclean things). 
Click here for a printable Shir Lamaalot card.
1. End of Sefer Raziel HaMalach, and elsewhere - [The Sefer Raziel HaMalach talks about an angel called Raziel and some attribute that book to Adam]. See Tishbi on the letter lamed, entry for “Lilith.” Plaques featuring the verses of Shir LaMaalot along with the Names [of G‑d and angels] etc. contained therein are well known throughout the Jewish world, each community having its own specific customs.
2. From the Sichah of 19 Kislev 5747 regarding things one should be careful about for the safety of the woman giving birth, including at the hospital [edited version printed in Hisvaadiyot 5747, Vol. 2, p. 37. Teshuvot U’Biurim BeShulchan Aruch, p. 446]: “It is fitting and proper to publicize everywhere that Jewish people live, the custom of hanging Shir LaMaalot.” See also the Sichah of Yom Simchat Torah 5737 ([printed in MiGevaot Ashurenu, p. 96]. See also Likkutei Sichot, Vol. 25, p. 309, where the Rebbe points out that “One should try to obtain permission from the hospital administration by explaining this properly, with words that proceed from the heart, which enter the heart and will certainly accomplish their task (and we point out that thank G‑d this custom is constantly spreading throughout the Jewish world).”
3. And obviously this will forestall any complications such as “…she had difficulty giving birth” [Vayishlach 35:16].
4. For even after the birth (during the first three days) she is considered to be a patient whose life is in danger, and we may violate the Shabbos laws for her [Shabbos 129a; Rambam, Hilchot Shabbos 2:13; Shulchan Aruch, Orach Chayim, and also the Alter Rebbe’s edition 330:4]
5. Sichot Kodesh 5737, Sichah 7 of Yom Simchat Torah; also printed in MiGevaot Ashurenu, p. 6, with the addition: “It is true that the child was just born, and cannot yet distinguish between light and dark or between sweet and bitter. Nevertheless, since he has already come into the world and he possesses eyes with which to see the world, we should see to it that before his eyes should be the letters of the aleph-beit, from whose combinations all of creation has come into being.” See details in Likkutei Sichot, Vol. 25, p. 309.