If you don't want to go the nuclear rocket route, and stick with technologies that are known to be physically possible and not require nonexistent materials....
If the planet spins extremely rapidly, such that you get a decent speed boost from equatorial launches and synchronous orbit is really low, then regular rockets and even space elevators may be suitable even for very massive planets, although rockets will be restricted in the inclinations they can reach. Earth is marginal for space elevators because the cable would have to be so long, and support so much of its own weight that there's nothing left for safety margin and payload, even with the strongest theoretical materials we know of. A higher spin, however, will lower synchronous orbit, potentially making elevators practical even with much higher gravity.
If you don't want to be restricted to high spin planets, you're left with basically one option: dynamic actively supported structures like Lofstrom launch loops and space fountains, possibly followed up by orbital rings (from which one could hang skyhooks in place of traditional space elevators). These kinds of structures make use of accelerating recirculating rotor materials inside their external static structure such that the reaction forces of the rotor materials on the static structure counteract its weight. This gets around the compressive strength limits of static materials, allowing you to raise platforms above the atmosphere and use electromagnetic tracks to accelerate to orbital or escape speeds in vacuum.
Of course, if you somehow manage to develop civilization on a planet with little or no atmosphere, you can just use electromagnetic launch tracks directly from the ground, coupled with low-power circularization rockets.