Just because no one speaks them anymore doesn't mean they aren't TOTALLY BADASS.
Akkadian
When: 2800 BCE to 500 CE (all dates approximate)
What you can read in it: The lingua franca of ancient Mesopotamia, Akkadian uses the same cuneiform alphabet as Sumerian. The Epic of Gilgamesh, the Enuma Elish creation myth and other texts were composed in Akkadian, which has grammar similar to classical Arabic.
Pros to learning it: How impressed will people be when you can read those tiny little wedges? I'd be impressed.
Cons to learning it: No one really speaks it anymore.
Source: cyberwitchcraft.com
Biblical Hebrew
When: 900 CE - 70 CE
What you can read in it: The Hebrew Bible, also known as the Old Testament, which was also later translated into ancient Greek (and then called the Septuagint.)
Pros to learning it: You can learn to point vowels, which is cool. Also, biblical Hebrew shares a surprising number of similarities with modern spoken Hebrew, including much of the alphabet.
Cons to learning it: No one really speaks it anymore.
Source: thebiblicalworld.blogspot.com
Coptic
When: 100 CE- 1600 CE
What you can read in it: The literature of the early Christian church, including the Nag Hammadi library, which contains the famous Gnostic gospels.
Pros to learning it: It's basically the Egyptian language written using the Greek alphabet, which is pretty cool.
Cons to learning it: No one really speaks it anymore. (Everyone switched to Arabic.
Source: ling.fju.edu.tw
Aramaic
When: 700 BCE - 600 CE
What you can read in it: The vernacular of Second Temple Israel (539 BC - 70 CE) and the lingua franca of much of the Near East for centuries, Aramaic is commonly identified as the language of Jesus. Much of the Talmud is written in it, as well as parts of the biblical books of Daniel and Ezra.
Pros to learning it: It's not that much different from biblical Hebrew, so you can kill two birds with one stone. Also, you can pretend you're talking to Jesus, if that interests you.
Cons to learning it: No one really speaks it anymore, save for a few modern Aramaic communities.