I assume that you are talking about the 3 "classical" states of matter - gas, liquid, solid. (There are also other, more unusual states of matter.)

The simple answer to your question is that all elements CAN exist in those three states.

However, that answer is not 100% correct. For one, there are some very heavy elements of which only a few atoms have been generated and which are highly unstable. For those elements, it doesn't make sense to refer to their state of matter because one would commonly think that to be a property of some amount of pure material. Then there is the question of what conditions are required to produce certain states of matter for some elements.

In many cases, it's simple enough, you change the temperature and the state of the element changes from solid to liquid to gas as the temperature is increased. However, pressure is a parameter that affects the state of matter just as temperature does, and some elements do not occur at one of the three states at our normal (ambient) pressure. An example is helium, which requires a pressure higher than ambient pressure to become solid.

A way to record the states (also called phases) are phase diagrams, specifically in this case pressure-temperature phase diagrams. These have been recorded for many elements and could be used to look up a specific element you might be interested in.

Phase Diagrams

All elements can exist in 3 states--if you can adjust the temperature and pressure they experience at will.

Let's unpack that starting with an element which is abundant and with which we are somewhat familiar: nitrogen.

Earth's atmosphere is made up of 78% gaseous nitrogen, N₂, so we know that the gaseous form of nitrogen is stable at room temperature (20 C for argument's sake) and atmospheric pressure (0.1 MPa = 0.1 x 10⁶ Pa, where Pascals are a unit of pressure). Liquid nitrogen is used as an industrial coolant (think early COVID-19 vaccines) because--drum roll--it is stable at low temperatures at atmospheric pressure (-196 C to be exact, and still 0.1 MPa). Nitrogen freezes solid at -210 C under atmospheric pressure. So if you could cool the nitrogen in the air down from 20 C, it would take a while but you'd reach the liquid's temperature at -196 C, and the solidus temperature at -210 C. But what if you could also change the pressure?

Hypothesize with me: At a constant temperature of -190 C (where gaseous nitrogen is stable at atmospheric pressure) would increasing the pressure change which state is stable? Hint: liquid nitrogen is more dense than gaseous nitrogen.

Did you say yes? If so, you're right! Increasing the pressure at this temperature tends to stabilize the liquid state of nitrogen. Now, if the density of liquid nitrogen is very similar to the density of solid nitrogen, what effect would increasing the pressure on liquid nitrogen at -200 C have? Did you say none? It's none! Increasing the pressure will not cause liquid nitrogen to solidify because of the negligible density difference between the solid and the liquid at -200 C.

We can conduct similar analyses for other elements, but it is important to note the following: just as equilibrium state (solid, liquid, gas) is a function of temperature and pressure, density is a function of temperature and pressure as well!