Is there any way of achieving effective thrust in space without using conventional fluid or gas propellants such as rocket-fuels or supercooled material?
For instance: gaining thrust through solar energy conversion or pressure pulses? (If that is even possible.)
There are a number of technologies for attaining velocity in addition to liquid propellants.
Solid propellants have long been a mainstay of rocketry, from the sole source of thrust for amateur rockets to auxiliary thrust the Shuttle. However, solid rocket propulsion is ultimately subject to the nastiness of the rocket equation, as is propulsion from liquid propellants. Moreover, even mediocre liquid propellants beat the best solid propellants with regard to specific impulse.
Plasma propulsion beats both liquid and solid propellants with regard to specific impulse. However, specific impulse is not the be-all and end-all that trivial analysis makes it appear to be. A very low specific impulse is obviously sub-optimal, but not so obviously, so is a very high specific impulse. Moreover, the thrust from currently available plasma propulsion systems is ridiculously small, and that "ridiculously small" is being very nice.
A nuclear thermal rocket (hypothetical) would use a fission-based nuclear reactor to generate heat, and this heat would be used to expel some propellant at a very high speed relative to the rocket. Other proposed forms of fission-based nuclear propulsion include project Orion, which would use nuclear bombs for propulsion. Fusion based propulsion has also been proposed, but these are just as far into the future as is fusion power, or Mr. Fusion.
All of the above are rockets, which means they subject to the tyranny of the rocket equation. There are a small number of techniques, ranging from purely hypothetical to proven, that completely bypass this tyranny. Solar sails don't carry propellant. They get thrust by reflecting light from the Sun. While photons are massless, they do have momentum. The IKAROS project demonstrated that solar sails do indeed work. The thrust is rather small, however.
Switching to the purely hypothetical side of fuel-less propulsion, there's the concept of a Bussard ramjet. A Bussard ramjet uses a fusion engine (which we don't know how to make) for propulsion. Instead of carrying the fuel with it, a Bussard ramjet takes advantage of the fact that empty space isn't quite empty. The interstellar medium has between 100 to 106 nuclei per cubic meter, most of which are either protons or hydrogen atoms. A Bussard ramjet would use a large electromagnetic field to capture this interstellar gas and funnel it toward the fusion engine. This is purely in the realm of science fiction for now, but at least it doesn't violate physics.
Since you mentioned liquid fuels explicitly, I feel obligated to bring solid-fuel rockets to your attention. They do not need to be cooled but once ignited, they can headly be stopped until they run out of fuel. Thus, they are primarily used as boosters to aid take-off. E.g. in the space shuttle, the thin white boosters attached to the orange liquid-fuel tank were solid-fuel boosters.
Of course, solid-fuel boosters also draw their power from the release of chemical energy. Ion engines on the other hand use electrical energy to accelerate ions (typically Xenon) across a voltage. The ions are expelled at high speeds which are not attainable by conventional rocket fuel, thus making them extremely efficient. The downside is that the thrust created by ion engines is really small, only on the order of a few grams. As a result, ion propulsion is used in deep space probes which are light and on a long journey. The electrical power for ion thrusters comes from solar panels and/or radioisotope batteries.
There are really not so many ways to propel yourself in space. It also comes down to expelling matter fast. The faster you do it, the more efficient is the engine. The curse of rocket science is the fact that you need to carry this matter along. There is the concept of a Bussard collector that has been popularized by Star Trek where you collect the hydrogen in the interstellar medium. However, the feasibility of this idea is doubted.
Recently, I read about a radically different engine design that would facilitate quantum vacuum fluctuations for propulsion. Apparently, NASA did some testing of this idea and found it to work conceptually.
Thrust is another name for force, and force is momentum per time. In other words, to get thrust it is necessary to generate momentum and to keep on doing it.
Typically it consists of projecting matter (gas, plasma) away from the vehicle, and the momentum transferred to that matter results in equal and opposite momentum given to the vehicle.
The faster the matter is projected, the less of it you need. That's why people are always looking for ways to project the matter with higher and higher speed. Of course, the required energy goes as speed squared, so as speed goes up, energy really goes up.
Another far-out way to get momentum is by projecting light, because photons have momentum, but that takes an enormous amount of energy.
Then you have to ask where does the energy come from, and that's another question.
P.S. @tpg2114 mentioned solar sail, which is a way to get momentum by catching the solar wind.
