Heat shields are only needed to remove the kinetic energy of an object that is descending into gravity well -- and usually to also remove the kinetic energy of its orbital velocity. There are many alternatives, but currently they aren't practical as they require too much fuel. For example, one to simply fire rocket engines until you are nearly at rest and then gently falls into the atmosphere... In such a case, the terminal velocity would be much lower, obviating the need for a heat shield. Unfortunately, this would also require a 'stopping' fuel load nearly as large as that which got you to orbit.

There has been work on nuclear powered rockets -- e.g. Minerva in the late '60's and early 70's but the perception of danger from accidents (i.e. dropping a reactor on an inhabited area) stalled this. However, such an engine could potentially have a large enough specific impulse to simply 'fly' into space. I.e. no need to orbit -- just keep lifting.

Recently there have been efforts to study the feasibility of an orbit elevator -- i.e. a 25k mile long cable with a weight on the far end, anchored to the ground. Cars on the elevator could be electrically powered and use the energy of descending cars to power those on the ascent. The cable would need to be long enough to reach beyond the geosynchronous belt (the distance at which orbital velocity is the same as the angular rotation rate of the earth). The only know material strong enough and light enough to make such a cable is Carbon Nanotube. Currently these cannot be made long enough to do this -- but many people expect that the length problem can be solved. Such a system could put objects into orbit space for a very tiny fraction of the energy expense (and real cost) now needed.

Yes - you need a series of several parachutes that will reduce your earthward velocity as you descend.There was a man during the 1950s who jumped out of a balloon at 80,000 ft elevation, essentially in vacuum,and that is how he did it. Of course, he was at rest relative to the Earth at that elevation, whereas something like a space shuttle is coming in pretty fast, so needs more than a parachute. You could also slow yourself down with engines. It's more practical to go with a heat shield, usually, or at least was during the Apollo program.

Yes, it's been done by SpaceShipOne. spaceshipone This plane wasn't going as fast as an orbiting spacecraft would be. It only flew up above most of the atmosphere and back. But the same principles could apply to a larger, faster craft. Basically, you need to find a way to slow yourself down without generating too much heat from atmospheric resistance. SpaceShipOne did it by tilting its wings 90 degrees so they were flat to the atmosphere--like a falling leaf compared to a falling dart.

If you have a long time (weeks or years), you can also just use the friction of the very thinnest, high atmosphere to start you slowing down to a speed where a ship like SpaceShipOne could then land safely. This is done for most probes we send to other planets. Instead of using a big rocket to slow down the probe once it gets to its destination, we use the planet's atmosphere to do most of the braking. We couldn't use this trick if there were people aboard, though, since nobody likes a flight delay of several months. :-)