Barometer

Piezometer
Open-ended tube connected to a vessel / pipe containing a liquid.
Measures the pressure head of a liquid.

Simple. Small pressure differences can be measured with it. Only works for liquids. A long tube is required to measure even moderate pressures.
Manometer

Hydrostatic principle is used here. Measures absolute pressure. Manometer liquid should not mix with the liquid in which the pressure is to be measured.
Differential Manometer

Used to measure pressure difference between two points. Can be used for both liquids and gases. Difficult to measure small pressure differences (because small displacement of manometer liquid).
Pressure Gauges
Bourdon Pressure Gauge
Easy to use. A wide range of pressures can be measured with it. Not very accurate. Needs to be calibrated regularly.