We can't really talk about Shadrach, Meshach, and Abednego in three separate character sections. They're a unit you need to take together, kind of like the Blue Man Group. Shadrach, Meshach, and Abednego are basically a lot like Daniel. They stick to their principles despite the accusations brought against them by the sniveling officials of King Nebuchadnezzar.
Their real names were (and get ready to fix up some coffee and grab a notebook), Hananiah, Misha'el, and Azariah. These names mean respectively, "God is gracious," "Who is like God?" (we're assuming that's rhetorical, and not the set-up to another Chuck Norris joke), and "God has helped." Shadrach, Meshach, and Abednego could mean, respectively, "Command of the Moon God," "Who is what Aku is?" and "Servant of Nabu" (Nabu is the Babylonian god of Wisdom and Nebuchadnezzar's favorite god). We're assuming that the answer to the question "Who is what Aku is?" is yet another tired Babylonian knee-slapper. It really is "Chuck Norris," this time. (Pfff—that's so ten years ago, Babylonians.)
Whereas we generally talk about Daniel using his Hebrew name—we don't call him "Belteshazzar" too frequently—we usually call Shadrach and co. by their Babylonian names. Why? Um, because those names sound cool. As another epic Hebrew trio, The Beastie Boys, realized a couple thousand years later when they rapped "We're just three emcees and we're on the go: / Shadrach, Meshach, Abednego."
So, what's so great about these guys? As if it were even necessary to ask. C'mon—they survive getting dumped into a furnace as punishment for staying true to God (a classic Metallica move). Moreover, they stick with Daniel and refuse to adopt a non-kosher Babylonian diet, surviving only on water and vegetables—which makes them wiser and way healthier than everybody else.
But back to the furnace thing, which is a first-rate Bible moment. (B.T.W.: if you haven't clicked on the link to watch the "Bunny Song" from "fiery furnace" themed Veggie Tales episode, this is probably your last chance).
When Nebuchadnezzar's about to order them thrown into the furnace for refusing to worship his giant gold statue of some Babylonian deity (probably named "Who-Cares-shazzar"), they're all like, "If our God, whom we serve, is able to deliver us from the furnace of blazing fire, and out of your hand, O King, let him deliver us. But if not, be it known to you, O king, that we will not serve your gods and we will not serve the golden statue that you have set up" (Dan 3:17-18). This is pretty much like shredding the riff to "Crazy Train" right in Nebuchadnezzar's face.
And it goes over about as well as doing that to someone really lame would go over. They get thrown into the furnace. But—to Nebuchadnezzar's surprise—they walk around in the furnace chatting with some mysterious person who has just appeared beside them (like an Angel or Jesus—if that's your preference—or somebody). Nebby is like "Whaa?" He lets them out, and says a bunch of pro-God stuff that he'll end up forgetting in about… five seconds.
So they escape. To quote the hypnotically upbeat conclusion to the movie, Tremors: "Way to go dudes!". These guys hung in there. They're more than a bunch of imitation Daniels who are just his side-kicks (well, we mean, maybe, if you want to get super-technical…). Shadrach, Meshach, and Abednego get promotions all around. So it ends up being a pretty good day anyway, even after all that furnace stuff.