Does the Sun have any atmosphere? Does the Sun have any atmosphere of its own? Is it just like the atmospheres that the planets have.
Yes the Sun has an atmosphere.

Disclaimer: I'm not sure if you meant this, but your question implies the Sun is a planet. It, of course, is a star and not a planet. Just wanted to make that clear.

What is an atmosphere?

When you ask if the Sun has an atmosphere, you're actually asking a tricky question. What do you mean by atmosphere? How do you define the boundary of the Sun, above which anything is considered an atmosphere? This is pretty easy for planets like Earth since they have a nice solid surface. But the Sun is a giant ball of plasma heated to thousands of degrees. There's no easy or clear division between the "surface" and "atmosphere". Any discussion of the Sun's atmosphere involves defining what we mean by the surface of the Sun.

Optical Depth

That being said, astronomers have come up with (arbitrary) ways to define the surface of the Sun. One common metric is to use optical depth. Optical depth is a unitless number that defines one's ability to "see" through a gas (or plasma). An optical depth of 1 or higher means the gas is opaque and cannot be seen through. An optical depth less than one means the gas is transparent and can be seen through.

However, when you have something the Sun or even fog, the optical depth varies with the distance you're looking into that object. I'll talk about fog since it's familiar, but the same idea applies to the Sun's atmosphere. Say you're standing in a forrest and its very foggy out. There's a tree 1 meter away from you that you can see. You could measure your optical depth, $\tau$, of the fog between you and tree and might find that $\tau = 0.15$. Since $\tau$ is less than one, that implies you can see the tree, but the value of $\tau$ also implies how well you can see it. If $\tau = 0$, there's nothing between you and the tree to impede your ability to see it. Let's say there's another tree that's 5 meters away. Now there's more fog between you and the tree and while you can still see it, it is harder to see it. The optical depth of the fog between you and the tree 5 meters away might be $\tau = 0.75$. It's still less than one, implying the tree is visible, but because there's more fog between you and the tree, the optical depth is higher. Finally, there may be a tree 10 meters away with so much fog between you and the tree that the optical depth is $\tau = 1.5$. You can't see this tree because there's too much fog in the way. Hopefully you now realize that anything which is at a distance where $\tau &gt; 1$ is not visible to you. That effectively defines a "surface" around you precisely when $\tau = 1$. Anything beyond that point is not visible and anything closer is visible.

If you're talking about the Sun, you can look at the Sun, but you'll only see light which originates from a point where $\tau &lt; 1$. There are countless photons bouncing around inside the Sun, but you can't see them because they're in an opaque part of the Sun. Astronomers use the optical depth as a metric for defining the "surface" of the Sun.

Keep in mind the above description is highly simplified, almost to the point of being wrong. The optical depth is a useful metric for defining a surface, but it doesn't imply there's an exact radius for the surface or even that the surface is constant for every wavelength. There are a lot of other factors that make this much more complicated than I'm describing here. Hopefully you get the general idea though.

The Sun's atmosphere

For the Sun, the atmosphere would be anything above the surface. Nominally the surface is defined as the point where the $\tau = 2/3$ (despite what I said above, and for reasons I won't go into here). The atmosphere above this surface is complicated and difficult to study. The atmosphere, just above the surface, is violent, turbulent, filled with outbursts and magnetic fields, and extremely hot. Below are some pictures of this region of the atmosphere.


 Left: Image of the corona during a solar eclipse. Right: Image of the corona from SOHO. An occulting mask has been placed over the Sun.

The atmosphere of the Sun extends far beyond that though. In fact, Earth is currently moving through the Sun's atmosphere. It's very tenuous out near Earth, but still exists. The Sun's atmosphere hitting our planet is the reason for aurora. Beyond the lower portions, the atmosphere is generally referred to as the Solar Wind. This solar wind actually extends far out, beyond Pluto even. Exactly how far is difficult to define, but estimates place our Sun's atmosphere extending out to about $\sim230\:\mathrm{AU}$. At that point is the bow shock, where our Sun's atmosphere slams into the interstellar medium surrounding us.

Our own Sun's atmosphere is hard to study on a large scale since we're inside it, but we have been able to observe this bow shock around other stars, as shown below.


LL Orionis bow shock in Orion nebula. The star's atmosphere collides with the nebula flow. Hubble, 1995