Suppose for a moment that cost would be no issue (and noone brought pruning shears) - could we build any of the non-rocket spacelaunch systems from earth listed here or elsewhere? Which one is the least unfeasable given current technology?
A light gas gun firing a G-force hardened booster seems like the best bet for lofting some sorts of payloads. John Hunter gave a presentation on the state of the art for this technology at this summer's Icarus Interstellar Starship Congress in Dallas:
Hunter's concept called for launching projectiles that fired a rocket near the apex of the ballistic trajectory to achieve insertion into LEO. His payload was fuel, to be collected in orbit and stored in orbital "filling stations." He formed a company to develop this commercially, Quicklaunch (now called TekLaunch), but was apparently forced out by his partners.
Nuclear pulse propulsion, aka Orion. There's little doubt it would work. The limits are not technological, but the fact that boosting an Orion means you're detonating a lot of atomic bombs in the atmosphere.
If you'll accept launches from other bodies the mass driver is the best answer. You can make the track as long as you like. Many years ago on TV I saw one that could boost a projectile to 100mph in six feet. If my understanding of the math is right that means you could easily scale it up to lunar escape velocity with a 3.2 mile track. Punching through the atmosphere is quite another matter, while a track a few hundred miles long could safely boost an astronaut to Earth escape velocity he wouldn't survive the passage through the atmosphere and the capsule would fall back due to drag anyway.
A rotovator rotating skyhook is within our technological ability - kevlar tether would be able to sustain it.
There are some important problems with the concept, of course. Besides the point that it would be very expensive to build (good 200-400km of kevlar tether shaped so that it can sustain itself against several g and keep tons of payload), expensive to maintain (subject to significant atmospheric drag, needs constant propulsion - although fuel delivery is no longer prohibitively expensive); the whole idea is nutty - the end of the tether dips into the atmosphere nearly vertically as the rotovator "rolls" over the upper atmosphere, and a perfectly synchronized airplane lands, or hooks a payload to it, right in the nick of time before the tip yanks it up and out of the atmosphere, then releases into an eccentric orbital trajectory. So the logistics of the operation are devilishly tricky - imagine a supersonic cargo aircraft, landing on an aircraft carrier which is a submarine that surfaces only for a minute or so.
The Wikipedia article you cited spells out your answer in the far right column of the comparison table. Technology Readiness Levels range from 2 to 9. Rockets (proven technology) score a 9. Gas guns and HARP canons have demonstrated amazing muzzle velocities and projectile altitudes in real hardware, so they rank 6. Almost everything else has a good theoretical background, small proof-of-concept models, and few obvious deal-breakers, but would require significant additional development, so they mostly score 2s. There is a chicken-and-egg nature to your question. If you are going to invest large sums in a launch system, you need to know what you intend to launch. Small packets of acceleration-insensitive materials like fuel? Gas gun or space canon would be great and are already at TRL6. Satellite constellations or space construction project sub-components? Now you need payloads in the 1 ton - 20 ton range and limited accelerations. I'm a big fan of Sky Tram and electromagnetic launch for that type of payload. I'm pretty sure we could adapt a lot of payloads to survive ~30g launch acceleration, which opens the door to an Electromagnetic launch system that's on the order of 130 km long. If you want to transport people in large quantities or payloads which can't be designed for high-gee acceleration, then you need to look toward spaceplanes and spaceplane/skyhook hybrid systems, which (in general) move larger payloads gently and infrequently.IMHO, given a few tens of billions of dollars most of the TRL2 systems in the table could be brought to TRL9. What is less certain is the reliability, durability, and ACTUAL $/kg these systems would achieve, and what specific goal they would support.
If we build small (few kilometers) Hyperloop-like booster in orbit, and use 'small' ground piece of Hyperloop to put aircraft into orbit altitude (200-300 kilometers), orbital part of the Hyperloop will catch aircraft and increase its speed to 7-8 kilometers per second. This concept is explained here – http://www.launchplatform.space