It is interesting to note that the tribe of Dan is also left out of the genealogies of I Chronicles 1-9, although the original son of Jacob is mentioned in I Chronicles 2:2. This historical point of interest helps explain why the tribe of Dan is not mentioned in Revelation 7:4-8.
The tribe of Dan as a whole was guilty of gross idolatry—even to the point of stealing the idols they used to practice their religion (Judges 18:14-31). Theirs was the first organized idolatry in ancient Israel, and the longest in duration. It continued "until the day of the captivity of the land," nearly 500 years later (Judges 18:30). Jewish tradition says that Dan was the first tribe to follow Jeroboam into his sin of idolatry, and in their literature, the term "Dan" is often used to represent idolatry.
From this summarized history of the tribe, it becomes obvious why Dan would not be among the 144,000 "servants of our God," as they are called in Revelation 7:3. Dan thoroughly rejected God's true religion for thousands of years, substituting a continuous tradition of idolatry. The end-time descendants of Dan say, "I have waited for your salvation, O LORD" (Genesis 49:1, 18). The vast majority of Danites must wait for salvation until after the sealing of the 144,000.
It is reassuring to know that Dan and all the other tribes of ancient Israel will be saved. In fact, Dan is mentioned first in the apportioning of land in the soon-coming Millennium (Ezekiel 48:1). The apostle Paul assures us, "All Israel will be saved" (Romans 11:26). The 144,000 are only a very small portion of the people of all nations who will eventually be saved.
A related question involves the tribe of Ephraim. Some have thought that this tribe is not mentioned among the 144,000 either, but Ephraim is indeed included. Notice that both the tribe of Manasseh and the tribe of Joseph are listed. Ephraim and Manasseh were the two sons of Joseph (Genesis 48:1). Since Manasseh is one of the two tribes descended from Joseph, "the tribe of Joseph" mentioned in Revelation 7:8 must refer to Ephraim. From this, we can learn that Ephraim, being the leading tribe of the house of Joseph, sometimes bore the name "Joseph."