I will separate this information into 2 main sections: V/UHF & HF. For most applications, the higher the better. (There are some cases, such as NVIS antennas, where you want the antenna relatively low.)
On the V/UHF bands, most communications are line of sight. That is, the RF signals do not curve completely around the Earth. They may bend a little at the horizon, but not much. You want your antenna up as high as you possibly can... SAFELY. Every 1 foot that you raise your antenna will allow you to hear approximately 1.6 miles further; if we go with the visual line of sight reference. Very simply, think of how far you can see at the ground floor of a building, then think of how far you can see standing at a window on the 20th floor, same simple idea. Basically, if you want to be able to talk and hear farther, get your antenna up higher.
There are other influences at work with RF signals that may somewhat obscure this. One item is foliage, tree leaves may absorb some of your RF signal between 2 radio stations. You may notice a difference when trees have dropped their leaves. If you get your antenna up above tree leaves it will help somewhat with transmission and reception. There is also multi-path, where as it's name implies, a RF signal may take 2 or more "paths" to reach you. For instance, you may receive a signal directly, and also the same signal may be reflected off of a side of a large building. These signals may add and cancel each other out at times.
On HF, we may inform another ham how high our antenna is above the ground in feet or meters. In many cases, to better understand how the same antenna may perform at different heights, we may speak of height in terms of wavelength. This wavelength is specific to a particular frequency (or frequency band in a looser sense). This is the same as stating to another ham that you have a quarter wavelength vertical antenna for 40M as opposed to a quarter wavelength vertical antenna for 10M.
For this next paragraph, let's assume our antenna is a 40M dipole, and that each of the 2 legs of the antenna is a quarter wavelength long. A quarter wavelength for 40 M is approximately 33'. Now if we were to have this antenna mounted at a quarter wavelength (again approx. 33') above ground, and were to compare the vertical radiation pattern with the same antenna mounted at one-half wavelength above ground, we would notice that the vertical radiation pattern where most of our signal goes, drops lower in elevation. This is what we want in many cases to improve our radiated power to be received by a foreign station via refraction in the ionosphere. The opposite would hold true for a NVIS (Near Vertical Incidence System) antenna. In that case, we would want as much of our radiated power to be sent straight up. More on NVIS antennas on this PAGE. Before I go on, I probably should have stated earlier, that one-half wavelength is double one quarter wavelength for the same frequency or frequency band. Again for 40M, a quarter wavelength is approx. 33' and one-half wavelength is approx 66'. Now if we were to raise the same antenna up to a full wavelength (approx. 132') we would notice that the vertical radiation pattern has dropped lower to the horizon in comparison to a quarter or half wavelength above ground.
PROVIDE IMAGES of VERTICAL RADIATION PATTERNS @ different wavelength heights.
These heights will change depending on what frequency band the antenna is designed for. An 80M quarter wavelength dipole (with each of it's legs approx. 66') would differ in terms of height as compared to the 40M quarter wavelength dipole. This 80M quarter wavelength dipole would be a quarter wavelength above ground at approx 66' instead of 33' for the 40M dipole mounted a quarter wavelength above ground. Again, our 80M dipole would be approx. 264' above ground for it's full wavelength height, as opposed to the 40M dipole's full wavelength height being approx. 132'. Conversely, a 20M quarter wavelength dipole (with each of it's legs approx. 16'), would be 16' above ground for it's quarter wavelength height, and 64' above ground for it's full wavelength height. So it can be seen now that the higher you go in frequency (lower in terms of amateur bands...80M to 40M to 20M), the more easily it becomes to mount an antenna higher in terms of it's specific frequency or band's particular wavelength. Not considering what band the dipole antenna is designed for, an antenna mounted @ approx 66' is a quarter wavelength above ground on 80M and a full wavelength above ground on 20M. In reality, an antenna when used on multiple amateur bands will have different radiation pattern characteristics depending on where in the frequency spectrum it is used.
Many of us are limited at to the height we can mount antennas. When choosing an antenna to use we would keep this height in mind for our selection criteria.
Effect of ground on antennas & their radiation pattern as they are increased/decreased above ground