The rocket equation is brutal, it doesn't take a world too much bigger than Earth before chemical rockets simply aren't going to do it. However, that doesn't mean they will be forever planetbound.
Nuclear thermal rockets can approach doubling the ISP of chemical rockets, thus permitting launch with twice the gravity well.
There's also the gas-core version of nuclear thermal--your reactor is gaseous uranium rather than solid. This more than doubles what you can get from nuclear thermal, again this doubles the velocity you can attain. The fairly narrow operating limits of a nuclear reactor make this design seem awfully scary, though!
Now we are into the dirty engines:
The open cycle nuclear thermal rocket--you maintain a chain reaction in uranium gas (probably UF6 to make it easier to handle), this is 2x to 6x the ISP over the closed cycle engine as you don't have to contain it. However, your used fuel becomes your exhaust--nasty for the environment and the crew picks up a substantial dose also.
Orion starts out at in the middle of this range. Again, your exhaust is hot. Bigger rockets have better performance, if they're big enough you can use boosted bombs and up your ISP still further. I can't find any estimates of the radiation exposure to the crew but given the numbers for the open cycle nuclear gas rocket I find this worrisome.
Finally, there are the non-rocket approaches:
First, the launch loop. You build two stations thousands of miles apart but at the same latitude. They throw iron bars back and forth. The bars never stop, when a station catches them they're whipped around with a huge magnet and tossed back, retaining their velocity. Note that the bars chase each other as close as possible, each will be drafting behind the one in front, the air drag isn't anything like what you would expect.
Once you have these bars flying back and forth you build a track on top of them--think of a maglev train but upside-down, the track is levitated on the bars, not the other way around. Of course this exerts a downward force on the bars but this is countered by speeding them up. The objective here is to get a good chunk of track basically out of the atmosphere. You can then mount a linear motor on it, your spacecraft goes up the track at sane atmospheric speeds, once it's clear of the atmosphere it hits the high power track and is boosted to orbit. The track must be massive enough to absorb the recoil without being knocked out of operation.
Huge, expensive and since it falls apart if any of the active systems fail it would be dangerous. However, the ISP is infinite as no craft resources are being used for the boost.
Finally, a solution that makes the launch loop look like a kids toy:
Build a maglev track around the world at the equator. Build a train on the track that has a maglev setup on top as well as the bottom. Make the track into an evacuated tunnel and boost the train to above orbital velocity. It's now exerting an upward force on the track which can counter the mass of the system. Build higher, build another train. Each train supports the mass of the section below it so the normal limits of how tall you can build do not apply--you can build out of the atmosphere and then resort to linear motors to push your spacecraft.
While again this is a dynamic system that collapses if it stops moving I don't think it's as dangerous as so long as you are using superconductors it's self-contained in the short run. If the power goes out it will continue to operate until the magnets quench.
Neither system could reasonably be built in a society with terrorists or madmen prone to spectacular suicides.