Virginia has the Virginia Breeze, which is literally intended to go places Virginia's state-supported Amtrak routes miss. So far it only has one line, from DC down I-81, but other lines are in the works.
from VA breeze website
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Maryland only
sort of qualifies. Its state-run transit agency, MTA, runs a commuter bus network that includes some lines that are more intercity in character, out to places like Hagerstown, St Leonard, Kent Island, and St Mary's County. Since MD is so small, between this and MARC rail really most of the state is covered. The far eastern & western parts gets left off. It's not truly a state intercity network, but it's so close I may as well mention it.
photo by so cal metro on flickr
You can see how it works on this map of DC-area long-distance commuter bus lines. It's the red.
map by peter dovak on ggwash
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Colorado clearly wins the award for best name, with its Bustang system.
photo by cdot
It's a pretty big system:
from bustang website