Blankets have four corners. So, do they require tzitzis?
In SHU"T SHOEL UMASHIV he answers that according to the MORDECHAI only when a garment is worn in a way of clothing (DERECH LIVISHA) is one obligated in Tzitzis.
The SHUT of the MARSHAM adds that Tzitzis are meant to surround one on four sides so you could see them when looking in every one of the 4 directions. A blanket does not have that, which might be the reason we do not put Tzitzis on our blankets.
The main reason quoted is that a covering which is made for use at night does need Tzitzs (Kesus Laylah) and a blanket's main time of use is during the night.
I think I remember seeing the Hazon Ish being Matir MeIkar HaDin to not place Sisit on the blanket.
Qiẓur Shulḥan 'Arukh - Yalqut Yosef (Oraḥ Ḥayim 18:9) states (my translation):
סדינים ושמיכות שיש בהם ארבע כנפות, אף שהאדם מתכסה בהם גם ביום, פטורים מציצית. ויש מי שכתב דנכון לחוש ולהחמיר בסדין של צמר, והמחמיר תבא עליו ברכה, אבל מעיקר הדין דעת מרן שגם בסדין של צמר פטור מציצית.
Sheets and blankets which have four corners, despite that one covers oneself with them during the day, do not require ẓiẓit. And there is one who wrote that it is proper to be stringent regarding a woolen sheet, and blessing should come upon one who is stringent. But, according to the letter of the law, the opinion of Maran [HaShulḥan 'Arukh] is that even a woolen sheet does not require ẓiẓit.
The Mishnah Berurah (Siman 17, S.Q. 8) brings, among other opinions, that of the Magen Avraham to round one corner to fulfill all opinions.
The Talmud (Menachoth, 40:1) says "Our Rabbis taught: A linen garment is, according to Beth Shammai, exempt from zizith; but Beth Hillel declare it liable. The halachah is in accordance with Beth Hillel"