Galaxies come in lots of shapes and sizes, but in general, we can group them into four flavors: spiral, elliptical, irregular (no real shape), and peculiar (definite shape, but weird).
We can also say lots of general things for each class: spirals are flat and have lots of gas and dust, ellipticals are spheroids with very little gas and dust, and so on.
The problem is, that pesky Universe of ours delights in throwing a monkey in the wrench. Behold NGC 4696, the confused elliptical:
[Click to galacticate -- and you need to, the above image doesn't give you any idea of just how freaking cool this image is!]
This two-and-a-half hour exposure Hubble Space Telescope image shows incredible detail. The galaxy NGC 4696 is the diffuse glow dominating the right hand side of the image. It sits in the center of the ginormous Centaurus galaxy cluster, a sprawling city of hundreds of galaxies about 150 million light years away.
Clusters of galaxies like this sometimes have one big, fat elliptical sitting in the center. Called the central dominant (or cD*) galaxy, it generally has far more mass than any other galaxy in the cluster and has weird features (like multiple bright cores, an extended halo of stars, and lots and lots of satellite galaxies). We think these galaxies started off relatively normal, but then eat other galaxies that wander too closely -- clusters are thick with galaxies, so such encounters are common. The now-heavier galaxy sinks to the center of the cluster through various forces, where it can really let itself go and eat even more galaxies. That explains the multiple cores (undigestible leftovers), their puffy halos (lots of orbital energy can be added to stars in the collision, inflating their paths), and the plenitude of little satellites (again, leftovers from previous galactic meals). If the one word "weird" works with cDs, then NGC 4696 fits this description pretty well. Note the dark swirl apparently near the galaxy's center, wrapping around it. That's a trail of dust 30,000 light years long -- 300 quadrillion kilometers (200 quadrillion miles) in length. It's very rare for ellipticals to have any dust at all in them, so seeing something like this really lets you know this guy is strange.
In the super-high-res image, you can see very subtle striations in the galaxy's innermost core. That's from ionized hydrogen, again very rare in ellipticals. Usually, all the gas is locked up in stars, and very little is floating freely.
Also, unseen in this image, vast amounts of high-energy radiation are flooding out of the galaxy's heart. This X-ray emission is clear in images taken by the Chandra observatory. Every big galaxy (even ours!) has a supermassive black hole in its core, with millions or even billions of times the mass of our Sun. In most galaxies that black hole isn't actively eating matter (to stretch the gourmand analogy a little more), so we don't detect it.
But if enough matter falls into the gaping maw, it can pile up just outside the point of no return, creating a huge disk of superheated material. Stuff that hot blasts out X-rays, and NGC 4696 is doing just that. Again, this all fits with the idea that it's been overeating; collisions with other galaxies can dump octillions of tons of matter into that central black hole, converting the normal galaxy into an active one.
Images like this one from Hubble are gorgeous, jaw-dropping -- and I haven't talked about the myriad background galaxies! But they are critical in giving us a big picture of galaxies. It's only by being able to get an overview of these beasts that we can hope to understand them. Like living beings, they are a complex interaction of smaller components, and if we don't get such a long view like this one, we're like the blind men and the elephant, only looking at one small part and making (erroneous) claims based on that.
Credit: ESA/Hubble and NASA
*A commenter below noted that the term cD is technically not short for "central dominant". I'm sorry I phrased it that way; I knew that, but the colloquialism, as I understand it, has rather taken over. My apologies for any confusion.