Claim to fame: Adopted dad of Jesus. Stands by his woman while she's pregnant.
Matthew's Gospel is Joseph's time to shine. Even though his story only runs through the first two chapters of the book, we're assuming he was in there changing diapers for years afterwards. He was a real hands-on kind of dad.
Joseph comes from pretty good stock. He's a descendent of both Abraham and David (1:16), which is pretty impressive. The fact that he comes from such a long line of Jewish patriarchs seals Jesus's claims of messiah-ship.
But, wait! Joseph isn't actually biologically related to Jesus. Before he lived with Mary, "she was found to be with child from the Holy Spirit," (1:18) remember? They never "knew" each other in the biblical sense (wink, wink). So, how can his lineage pass down to Jesus?
Well, it looks like Matthew is just using that genealogy to add icing to Jesus's messianic cake. His family descends from a long and proud line, so Jesus does, too. Right? Plus, Joseph took responsibility for the child and raised him as his own, so it's possible some of that good DNA rubbed off….
You know what? Just try not to think about it too hard.
Speaking of taking responsibility, Joseph really takes charge of the situation with Jesus. When his fiancée comes to him and says she's pregnant, Joseph doesn't want to "expose her to public disgrace" (1:19), so he does the noble thing and plans to break it all off on the down low. What Mary does with the baby is her own problem though, we suppose.
Luckily, an angel of the Lord appears to him to let him know that everything is cool. In fact, dreams and angels are Joseph's primary way of making major life decisions:
God just loves popping in during people's REM cycles.
You'll generally see Joseph hanging around in artwork featuring the baby Jesus. In olden times, he was usually portrayed as an older guy with gray hair. Kind of creepy, since Mary looks like a teenage girl in those same paintings. Today, it's much more common to see a youthful, hands-on dad type Joseph. He's often got a hammer in one hand (because, as Matthew points out, he's a carpenter) and tiny baby Jesus in the other. What a multitasker. (Source.)
In the Catholic Church, Joseph is the patron saint of dads. And for some reason, there are people who think that if you bury a statue of St. Joseph upside down in your front yard, you'll be able to sell your house quickly (source). Apparently the guy was a real estate agent, too.