There are many types of antennas used on HF, and they can be broken down into 2 types: Directional and Omni-Directional.
Omni-Directional
There are not many of these antennas, because most antennas focus the radiated energy in a specific direction in some way. These are very common portable and first antennas for hams on HF. Because most do not need a tower or lots of real estate.
Vertical
Vertical antennas are very popular antennas because of their radiation and take-off angle characteristics. These antennas usually cover 6-40 meters and lower bands with the use of loading coils.
Common Variations: Inverted L, Vertical Dipole
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Inverted L
An inverted L is a type of vertical that is extra long. People tend to use these on low bands like 80 and 160 meters because a vertical on these bands would be so tall it would be unmanageable. READ MORE HERE
End-Fed
The end-fed antenna is very popular because of its multi-band characteristics, cost, and ease of setup. These antennas tend to be multi-banded and require the use of radials. These tend to be omnidirectional but can be somewhat directional based on how they are installed. They use an RF transformer at the ‘base’ of the antenna to match the impedance of the wire to 50 ohms.
Common Variations: Zepp, Random Wire,
Dipole
The dipole is a common first antenna because of its simplicity, cost, and good performance. It is relatively omnidirectional, but has some gain front to back vs side-to-side.
Common variations: Off-Center Fed Dipole, Doublet, G5RV, Vertical Dipole
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Directional
Directional antennas are very popular in amateur radio because they enable Gain. Unfortunately, they are more complex and expensive to set up. But they also provide the basis of an effective HF station. Learn more about antenna gain here: ANTENNA GAIN
Directional antennas also work best pointing in the desired direction. That is why antenna Rotators or Rotors are used. More on those here: ANTENNA ROTATORS/ROTORS
Yagi
Yagis are the most common DX and contesting antenna. Unfortunately, they are large and
Loop
Delta Loop
Cubical Quad
Log Periodic