You have to check the datasheet for the specific regulator. Some require a certain level of resistance in series with the capacitor, and recommend electrolytic (or tantalum) capacitors due to the high ESR. However, ESR is specified as a maximum, and future capacitors with far lower ESR may still be within their own specs but have too low ESR for the loop stability.
These types can be used with ceramic caps, but to ensure stability, it is necessary to put a small series resistance (typically <1ohm) in to ensure stability. Other LDOs are specifically designed to be stable with ceramic caps.
Note when using ceramic caps that you won't always get the capacitance you're paying for. Using class 2 ceramics for supply bypass is worst case in that your AC voltage across the cap is minimal (lowering the capacitance) while the DC voltage is probably close to the rating (further lowering the capacitance). This is a good tool to see those effects...ceramic chip caps will behave about the same for the same size and value from different vendors.
Although as a general rule more capacitance means better performance, each regulator has its own idiosyncracies. Also remember that the output capacitance doesn't just include the capacitor closest on the schematic...it includes all the bypass caps connected to that supply.