@Cruithne:
The Red Line is impassable unless you use Reverse Mountain, Mariejois, or the Fishman Island route. You can't climb over it.
Barring Sanji (whose being in the East Blue hasn't been explained yet) everyone in the SH that wasn't from the East Blue joined in the Grand Line, rather than their respective oceans (aside from Chopper).
Reverse Mountain doesn't appear to… well... work in reverse. With the way the currents flow, it doesn't look like you can go from the GL back to one of the oceans that way. You can't go through Mariejois unless you have government permission (which bars all pirates ever), so the only way you could hope to pass the Red Line is by going under it, which has a high risk of death and isn't very practical all things considered.
If you're a marine, you can get permission to go anywhere with relative ease, but you're stuck following someone else's orders. If you're a pirate, you can go where you want when you want, but you're going to need to face the calm belt to leave, and to dive underwater if you want to get back to the North or West Blues from the Grand Line. If you're a regular Joe and just want to travel, you're going to face the same problems pirates face, but with added danger of pirates pillaging your stuff.
Tl;dr: You could travel in spite of the Red Line, but it'd be a big pain in the butt and more trouble than it's worth (either from not getting to do what you want or being in constant danger). And you'd probably wind up dead.
Pappug implies that anyone but Pirates can use the Mariejoa path.
And even then, like Aaronrules pointed out, the other blues could still have their own passages.
@Cruithne:
There'd still be trouble going between from the north to south equators, though. You'd still have to go through two calm belts and the Grand Line to do that.
Then just walk down the Red Line until you're in the opposite equator.
The logic would be like arriving at N. America from the N. Atlantic/Pacific ocean, crossing Central America, and getting into the S. Atlantic/Pacific ocean from S. America.
Travel time would be long and probably very expensive, but it's still better than Sea Kings.
I'm assuming there's some sort of elevator system that brings people up to the Red Line, which seems to be the case with the Mariejoa path.