Usually bell peppers ripen red, orange, yellow or less commonly, brown. Most green peppers that you eat are actually unripe ones that ripen to other colors. Some peppers ripen green, but that is rare.
To quote farmerdill on gardenweb, "Just after WW II several green when ripe varieties were introduced to extend the market window." The two green-when-ripe bell pepper varieties I know about are Permagreen and Staysgreen, although evergreen chili peppers exist, too, including, but not limited to, Green Fatalii (PL), Green Moruga scorpion (PL), Evergreen 7-pot pepper, and green habanero.
Now, maybe you're of the opinion that even the green when ripe peppers are unripe, and they just stay unripe longer. However, this contradicts the claims of those peppers, which are said to be like ripe green tomatoes in that regard. Notwithstanding this, however, there actually are peppers that just stay unripe longer, but I have no reason to believe the ones I mentioned are anything like those, and there appears to be little evidence to support or contradict either claim. If you can find some Permagreen seeds to verify the claim, you're fortunate. I contacted a previous seller of the seeds for more information. We'll see.
EDIT: The seller replied. Apparently, they did list it once, but they never actually sold any because they either weren't available or they didn't germinate. If they didn't germinate, that contributes to the idea that they just stay unripe for a long time, although it's not definitive proof. Anyway, you'd think if they did ripen green that people would still grow them, today. Whatever the case, you can always breed a real green-ripening bell pepper using one of those green-ripening chilis in a breeding program. It might take a while to get the bell pepper shape back and the spiciness out, though, but it's possible.
EDIT: sandhillpreservation.com sells Permagreen pepper seeds. Here's their description: "79 days. An introduction of Dr. Meader that stays a deep, black/green without ever turning red."
It should also be noted that the Green Habañero does get slightly yellow when ripe (but it's still supposed to be green). Many green-ripening tomatoes do, too, if not completely yellow (but they're ripe enough to eat, and probably save seeds, before that point), but Baker Creek makes the following claim about at least the Green Giant tomato: "Color stays pure green even when dead ripe!". Similar claims were made about some of those hot peppers I linked to above. We'll see about Green Giant and Green Zebra tomatoes this year, however, since I'm growing them. I'd like to get some of those peppers soon, too.
Edit: I grew Green Giant tomatoes, and it's true. They stay completely green. They don't yellow at all even when they're soft. They're also one of the best-tasting tomatoes I've tried. However, they're not heat-tolerant, and mine were prone to cracking when ripe. They're very juicy, and they were not at all sour. However, I did give them extra potassium, and potassium is supposed to make tomatoes less acidic, I've read. I grew Green Zebra, too: it does yellow a bit when ripe.
Some people say pepper colors are much like tomato colors. If they are right, the explanations for green-ripening tomatoes may also apply to green-ripening peppers. See this link about tomato color genetics.