Lots of good answers here, so I'm not trying to outdo anyone (especially since I am not a native speaker of Spanish). What with so many different names for beans, though, I really started getting confused about what name for bean was used where. More importantly, I thought it would be helpful to you, myself, and others reading this post, if I could find a way to figure out which ones would be most useful to learn.
Clearly, if you know you'll be visiting a certain region then you'll want to focus on vocabulary particular to that region, but for the vast majority of us who won't be traveling to foreign lands and simply want to be able to take our Spanish to the next level, I thought it might be useful to rank these various beans on what their frequency is in online Spanish newspapers. So, I took all (or nearly all) of the bean names listed in this thread and then also the ones listed in
(Big thank you to Nicolás for including it in his answer, otherwise I might not have ever visited it.)
I then filtered for language (Spanish) and type of page (News). I made sure to set the query up to return results for both singular and plural forms (though you will just see the singular listed in the charts below) and added other measures to ensure that what was returned were pages about beans and not something else. It wasn't an exact science and, for at least one word (blanquillos*), I had to fiddle with the query a bit to make it work, but, if you don't want to learn the nearly three dozen names for beans that you will see between this thread and the Wikipedia article I referenced, and just want to focus on those you might see as you start getting to a point where you can read Spanish news articles, the charts below might help.
*If you type in "bean" into any online English-Spanish dictionary/translator, I doubt any of them will list "bean" for "blanquillo." Term Bank did not and neither did WordReference. But since the Wikipedia article mentioned that "blanquillos" was, indeed, the name for beans in Colombia, I did my best to find some evidence that "blanquillo" is used as a word for "bean," and was able to do so. To back up a bit, Term Bank does list some meanings for "blanquillo." Among many other things, it lists "small fish" (in Chile) and "chicken egg" (in several others). Despite the fact that Term Bank mentions it is little used as "chicken egg," I saw several images of eggs surface in my search for "blanquillo." Most of the initial images were of fish, but I'd have to say that the second most popular image was that of what appeared to be chicken eggs. Regardless of how frequently people use it for that, I was also able to find at least one image of it as a product that might be sold in a supermarket (other than an egg ... or a fish). Here it is:
Here you can see that "blanquillo" is prefaced by "frijol," but it appears that this type of bean is often simply referred to as "(los) blanquillos." Take note of the print at the bottom and you'll see that the product uses a Colombian address on its packaging, which corresponds with the information included for this type of bean in the Wikipedia article mentioned.
As for the rest of the beans, I tried to use an image of the bean that was most representative. If the word was just a generic name for the bean, I used a generic image (the sacks of beans). I know that some generic words for beans sometimes refer to a specific variety of bean in certain regions. For example, Javier above mentions that in Puerto Rico, they used "frijoles" to refer to "black-eyed peas." So, please keep that in mind as you look at the charts.
The word "haba" is a bit different than the other beans in the chart above. In the Spanish Mediterranean, "haba" is used for the Vicia faba, which you may know better as the broad bean, fava bean, or even lima bean (habas verdes). Although technically, the lima bean's actual Latin name is Phaseolus lunatus, which makes it a different species of plant altogether, but still in the same family (Fabaceae) as the "haba." In colloquial usage there may be some overlap in naming conventions for these different types of beans.
Perhaps the main difference is that the one (the "haba") originated in North Africa and the other (the one English speakers call a lima bean and that Spanish speakers might refer to as a "pallar," a "guaracaro" in Venezuela, or simply "frijol" or "haba" elsewhere) originated in South America. They look very similar, so it is not surprising that they are mistaken for one another, but they differ somewhat in appearance, taste, and composition. From personal observation, I notice that the lima bean tends to have a grainier appearance than the fava (or broad bean). Below is a side-by-side chart of the lima bean and fava bean so that you can see how similar they look:
From a nutritional perspective, a cup of lima beans will give you, cup for cup, less fat and almost twice as much potassium, but fava beans will give you more protein, more calories (and quite a bit more fat), if data collected from this source is correct. (Data for lima beans collected here; data for fava beans collected here.) I put some of the data in a chart so that you can compare them yourself: 
I've never had a fava bean, so I can't describe that to you, but a couple of people do so in this thread here: "What is the difference between fava beans and lima beans?
In the rest of the Spanish-speaking world the "haba" is a common dry bean and though you might not see it paired with "blanca," it is paired with "negra" (for "black bean") or "roja" (for "red bean"). Keep in mind that the other names for bean listed in the chart above are far more commonly used and paired with descriptions of color to differentiate specific types of a dry bean. The word "haba" is also known by many as the word to use for "coffee bean," but there are others. More on that later at the end of this answer.
As you may have noticed, where I could fit them in, I also added product images. There's nothing quite like seeing actual merchandise to help remember a foreign word for something. I can't buy everyone a plane ticket to every Spanish-speaking country in the world, but this is the next best thing.
I did not include four words found in the Wikipedia article — calbotes, balas, balines, and ejotes. I just couldn't find strong enough evidence linking the first word — calbotes — to the word "beans," despite the article's claims that "calbotes" is the word for beans in Navarra and Tierra Estella (regions in northern Spain). Both "balas" and "balines," words claimed to be used in Honduras by the aforementioned Wikipedia article, just seemed too difficult to try to dig out from all the pages where these mean "bullets" or "pellets." Leaving "ejotes" off the list was simply an omission of error. If you are interested in reading articles from news outlets in Guatemala, Honduras, and Mexico, you will likely come across "elote" from time to time, especially if you read a section devoted to food. This word for bean refers specifically to "green bean," and had I included it, it would have fallen between "chaucha" and "pocha" in terms of prevalence found in online news articles. In other words, it appears to be more prevalent than "chaucha" (another term for "green bean") and "pocha" (a different type of bean) and would mean that were it not somewhat exclusive to the three countries already mentioned it might be considered the most universally recognized word for "green bean." But as it is, I believe "judía verde" or simply "judía" is the word most Spanish speakers (and students of Spanish) are most familiar with for the vegetable we refer to as a "green bean."
The last thing I want to mention in this post (and I'm rather shocked it wasn't brought up yet ... ) is what word for bean should you use when you want to say "coffee bean?" Reverso seems to prefer "grano de café" as does WordReference. You'll find that and more (including the previously mentioned "haba") if you search for "coffee bean" with Term Bank.
Source Notes: Nothing other than what has already been given, except for attribution for the image of the caparrones that was used in the second chart above. Attribution is as follows:
De Xufanc - III 2011, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=14790785
As for the other images, I did my best to make sure they didn't have a copyright on them and/or weren't produced for the purpose of attempting to make some sort of profit off of them. That is to say, I attempted to preserve intellectual property rights and avoid encroaching upon someone's interest in obtaining compensation for their creativity, talent, or efforts.