In North India - Tuesdays are dedicated to him because Hanuman is believed to bring Mars (Mangal) under control. Mars being an aggressive planet it is necessary for a "stronger" god to keep him in check.
Down south, Hanuman worship is more on Saturdays - as it is the day dedicated for Vishnu and his incarnates - hence Rama Doot also gets his share of attention. Also he is known as the "Siriya thiruvadi" - meaning the "Smaller Feet/Vahana" and during weeklong festivities the lord is taken out on Hanuman. (Also known as Hanumantha Seva - popular in Tirupathi) (Garuda is known as the Periya Thiruvadi - or the Primary Vahana of the Lord.)