For in-system travel, most large ships use impeller drives, which manipulate the local gravity field around the ship, allowing for fast straight-line acceleration and relativistic velocities. The drawbacks of the impeller drives are twofold: first, they are not very maneuverable. Small, technical maneuvers put dangerous stress on the hull if performed with impeller drives, and captains have been known to tear their ships in two trying it. Second, and perhaps more importantly, the energy requirements of impeller drives are enormous. Large ships outfitted with impellers also must carry a Helium-3 fusion reactor on board. Running the reactor produces a detectable neutrino signal, making it impossible to hide a ship with impellers, even on the far side of a planet.
Ion propulsion engines of various types are used for fine maneuvering as well as “stealth” operations. They aren’t capable of anywhere near the velocities of impeller drives, but they have a high specific impulse and they are small and lightweight and can be placed at various points along a ship.
Atmospheric travel is accomplished with a variety of air-breathing engines, since ion propulsion doesn’t work in a planetary atmosphere. Most of these are evolutions of the thousand-year-old jet engine, characterized by highly efficient superconducting motors and high-altitude hypersonic scramjets. Pinnaces, designed for travel between space-only craft and planetary surfaces, are usually outfitted with a combination of superconducting jet engines, scramjets, and ion engines.
Most interstellar travel in facilitated by FTL “jump” drives, which currently have a maximum jump range of about 20 light years. The jump drives are essentially probability drives, using the quantum probabilities of matter to instantaneously teleport a ship from point A to point B. As you can imagine, the computational power necessary to calculate such a jump is immense, and it is the primary limiting factor in the development of FTL technology. Current technology requires a waypoint beacon to guide each jump, which means ships must jump to and from set locations in space. The waypoint beacons have much more computational power than a single ship has, and are able to relay jump coordinates to a ship’s FTL drives and facilitate the jump. Attempting to jump without a waypoint beacon—blind jumping—is risky business. Most of the time it ends up in the matter of the ship being probabilistically scattered over a 20-light-year radius.