At 1G to Jupiter you save a second due to special relativity. dope.
Celestia is still alive, BTW.
I once had a prof take our class through the 1G acceleration calculation for getting to the galactic core. What I remember most was the amount of energy you'd need to accelerate/decelerate a decently sized ship. If you assumed a perfectly efficient engine with an anti-matter reserve you were converting to energy (via E = mc²), the mass of anti-matter needed was something on the order of Earth's mass. And that's why when people talk about intergalactic exploration in our species' future, I don't get too excited.
Savage. Such things shall be accomplished through VASIMR and Bussard ramjets. Only peons would lug their own fuel around! And yes I know that VASIMR doesn't get around this problem don't interfere with my dudgeon! At some point several years back some wonk pointed out that we have no reason to assume the interstellar medium is uniform and that, erm, local space around us might actually be kinda lean. So... you could fire up your ramjet, set sail for the second star on the horizon and then flame out 400AU past Pluto. I think Robert Park used to do the 1G-to-Alpha Centauri schtick with like a VW Beetle. Even that took an appalling enough amount of energy that nobody asked him about manned space flight for the rest of the quarter. For my part, having watched an office building full of LOX launch a satellite the size of a Honda at the cost of a Nimitz-class aircraft carrier, I've become a lot more jaded about leaving the stellar nursery myself.
There's also the classic warp drive. I'm not sure that it's possible, but unless we come up with a way to extract energy from spacetime itself, I don't think we'll ever manage intergalactic travel. Hah, now that I think about it, if we ever start testing experimental builds for such machines, I'd like to have some legislation mandating that they're only turned on ~10 light years away from humans and with a trajectory that takes them out of the galaxy.
Well DUH the first thing you do is develop a Kardashev (II) civilization and methods for synthesizing exotic matter and then you go out and scoop about for micro-wormholes and then you send one end out where you need it to be and then you dump a black hole's worth of energy into both sides and then you just walk right through it. And then it doesn't matter how much reaction mass that fucker Tsiolkovsky thinks you need to get up to speed because you're already sitting on a purple beach under a Vegan sun sipping Romulan Ale mai thais. I may or may not have sold this screenplay.