Catastrophic failure
A Catastrophic Failure is an event that makes it impossible to finish the mission, usually either killing the crew, stranding them in space or forcing them to initiate a reentry using the engines and fuel they didn't lose in the accident. When testing new spaceship and spaceplane designs, catastrophic failures are nearly unavoidable, but unexpected events can happen even on thoroughly tested designs.
Failures of Design
Staging Sequence
A very widespread cause of catastrophic failures is incorrect staging stemming from an oversight when arranging parts into stages. This can result in engines igniting prematurely and damaging the spacecraft, or stages decoupling too soon, depriving the ship of essential fuel reserves. The most destructive is having engines or boosters in the same stage as their decouplers. This will result in the engine igniting and being separated at the same time. Radially mounted boosters can tear off parts of the ship as they accelerate and base mounted engines will start pushing the craft uncontrollably forward, or ramming and tearing it apart. A special subset of this failure is the TT18-A Stability Clamps not disengaging because they are not in the first stage. This will often just bind the ship to the ground without endangering the crew, but the loss of fuel will doom the mission before it starts. On rare occasions the clamps can tear your craft apart given a high enough TWR.
Fix
Though very frustrating, this is the simplest problem to correct. The player just has to rearrange the parts into their correct stages in the VAB. Since all the decouplers have the same icon -except for the radial ones- one has to point the mouse at them and watch which part of the ship gets highlighted. Make sure that no engines are in the same stage with their decouplers and that the decouplers on the ship and in the list are in the correct order to avoid jettisoning stages prematurely.
Breakage and Detachment
The parts of a spacecraft have a maximum tolerance threshold for staying connected. When they are put under a large enough weight or acceleration the connections can break under the stress, making your craft fall apart. It is difficult to predict in advance where these voulnerable points will be, though experienced ship designers can identify some of the more obvious ones. Sometimes though you will only spot these weak ponts when your craft breaks apart or just falls down on the launch pad without ever taking off.
Fix
Struts, especially the EAS-4 Strut Connector, are your best friend in this situation. The most obvious points of breakage are usually around decouplers where two powerful stages are connected only by a decoupler ring. Multiple struts that connect the lower and upper stage around the decoupler should resolve the issue. Another problematic structure is an engine nozzle on the end of a long line of fuel tanks that are connected to each other or a center part by the uppermost fuel tank. The thrust generated can pull these columns apart and make them wave around often hitting and damaging each other. Use struts to tie the lower ends together just above the engine to stabilize the structure.
Steering
Every part has a drag and mass value, and some have lift ratings. Sometimes you want lift, mass, or drag on certain places (especially on airplanes) but in others, these three values may wreak havoc on your rocket/spaceplane if used incorrectly, either setting it into a spin or tilting it in wild directions.
Fix
Use the three Mass, Lift, and Thrust buttons (located to the left side of the parts) to see where lift, drag, and thrust are centered. In the average rocket, these should be more or less linear, with the Thrust arrow pointing straight up. In an air/spaceplane, it's a bit different-The center of mass and lift matter a bit more (though you should still see if the thrust is centered.) The lift arrow should not tilt left/right in relation to the craft, and the mass should be in the center (and preferably nearer the back.) Once you've got these down, add a S.A.S Module and/or an Advanced S.A.S Module module for extra stability.
Failures in Flight
Accidental Staging
Sometimes the design is not the cause of failure. The most widespread problem is likely accidental staging. The player pushes space by accident and decouples a stage when he/she doesn't want to. The most destructive of all is the decoupling of a lower stage when the engines haven't finished their burn yet. The resulting difference in acceleration between the decoupled half and the upper intact half can cause the former to ram into the latter, tearing it apart and often killing the crew.
Fix
Pressing the lock stage key combination (default Alt+L) will toggle locking the stages. The green light below the stage list will turn purple, letting you know you have locked the stages.
Ion-powered, Solar-powered & Unpowered
This is a problem which rarely becomes obvious to the player until after the vessel has entered orbit. To put it simply, the solar panels have been placed in such a way that they provide insufficient power when the craft is facing a certain direction, this is of course disastrous for ion-powered craft which require a steady flow of electricity, and frustrating for drones which cease to function when they run out of power.
Fix
There are three ways to solve this problem, one permanent, another which require occasional corrections to the vessel's position on its roll-axis, both require the vessel to be brought back to the VAB/SPH or, if the vessel is equipped with docking ports, the addition of new sections with properly attached solar panels.
All sided
You can place 3 solar panels, one of them should face forward, one rearward and one should be pointing out from the side of the vessel, by rolling the craft so that at least one of the panels is exposed to the sunlight, it can generate enough power to allow use of basic electric systems such as unmanned command modules, lights and other low-power systems.
Targeting panels
You can use the moving solar panels, this means that you will only need to mount one panel which turns itself on one axis to follow the sun, while you roll the entire spacecraft to turn the solar panel in the other direction, allowing maximum-efficiency-harvesting of sunlight no matter where the craft is pointed.
Batteries
Place batteries on the vessel and use their power when the solar panels are pointed away from Kerbol. This is not an actual solution, and if you are using an ion engine, it is most likely better to cancel the flight and build a new vessel, but your craft will still be able to operate lights and unmanned control modules for a short time after the solar panels have ceased to produce power.
Not enough Fuel
Every vehicle has two purposes: To make sure something gets somewhere to do something, or to make sure that something is kept away from somewhere to ensure that something bad doesn't happen. Either way, a spaceship requires fuel to do what it should, and sometimes your brave kerbals will find themselves in a spaceship with empty fuel tanks, unable to go where they want to, or unable to keep their vessel from going where they don't want it to go.
Fix
- Keep a close eye on the fuel/oxidizer levels, if you are about to run out of fuel before you can complete a manoeuver, either leave the craft where it is and send up another to refuel it, or de-orbit the vessel and try again, less debris means following expeditions are less likely to be rammed by old rockets.
- try to put at least one docking port on every ship you want to keep, this means that you still have a chance of reaching the stranded craft with a "tanker" and refuel it.
- Use the RCS to finish the manoeuver, unless you're flying a very large vessel with very small RCS-fuel tanks, there should be some left, not enough to let you complete the mission, but hopefully enough to de-orbit or to move the vessel into a favourable position prior to docking with a refueling ship.
- "would it help if I got out and pushed?". Good question, and in KSP, the answer is yes.
As command modules carry around just enough rocket-pack fuel to refill a kerbonaut's rocket pack for all eternity, one can actually do an EVA by using a kerbonaut to adjust the speed and heading of tiny spacecraft. Just remember to get your little friend back inside the capsule and deploy the Chutes before they both enter the atmosphere of any planet you've decided to land on.
Failures on the surface
Flat tire
Driving too fast or landing a rover at too high speed may cause rover wheels to pop, if you have seveal wheels on your rover, the loss of one may not be the worst thing to happen, but if your rover has too few wheels to keep rolling afterwards, a flat tire will mean the end of the entire mission.
Fix
The best way to avoid flat tires is to drive (and land) with care. If your brave kerbals still find themselves looking at a flat tire now and then, it is still possible to repair the wheel. Take one of the crewmembers for an EVA, get close to the wheel and right-click on it. You will be showed a small menu with the option to repair the wheel. If you do not have any kerbal available to perform the task of restoring the wheel to its former condition, you can usually send a single-seat spacecraft with a technician to land near the immobilized rover, if even that isn't an option, then you may consider using the torque from the control module to keep the damaged wheel off the surface while driving.