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One reason is to remove some of the indigestible complex sugars that cause gas.

Another reason is that beans are dirty, so you're just cleaning them with the soaking. If the recipe wants the beans to be cooked in the water used for soaking, the washing needs to be done before the soaking.

On top of that the soaking can reduce cooking time considerably, which might be the biggest advantage.

Mark Bittman distinguishes three techniques:

Quick-Soak (boil, turn off heat, let soak 2 hrs, return to heat, simmer til done), No-Soak (boil then simmer, til done), and Long-Soak (soak in cold water for 6-12 hrs, drain, simmer til done). (taken from here)

The cooking time of beans varies from bean to bean. Bittman prefers the "quick soak" variant, and it is easy to see why: For most beans, it significantly reduces the cooking time (and thus the time you need to watch the pot and presumably the energy), and it doesn't require you think of soaking beans the night before. If you are happy and get good results without soaking, I don't think there's a compelling reason to switch.

As others have said, soaking mostly decreases cooking time. That's the main reason to do it. With some beans, the difference in time is minimal, but with tougher beans that take longer to cook (e.g., black beans), soaking can reduce cooking time significantly, particularly if the beans are a little older and more dried out.

The reason is because the first period of time in water is spent hydrating the seed coat. Once the seed coat is completely hydrated, water can flow through the surface and begin to cook the interior of the bean. The hydration of the seed coat can happen in cold water as well as hot water, so soaking beans will allow that process to begin before cooking. With most beans, the difference in cooking time might be 15-30 minutes (perhaps not enough to be significant for a dish that's cooking for a couple of hours anyway), but with some it might be as much as an hour.

Some say that soaking helps to maintain shape or keep beans intact, but I've found that really depends on the type of bean, how old they are, and how they are cooked. In many cases, the best-looking beans I've made have come from batches that were never soaked but cooked slowly (start in cold water and slowly bring up to a simmer).

The other main reason often cited is to prevent flatulence. However, if you throw out the soaking water, you also throw out lots of nutrients. Recent research suggests that long slow cooking is a better solution and probably gets rid of more of the flatulence-causing components than a soak followed by a quick cook. And you get to retain more nutrients. To quote Harold McGee from On Food and Cooking:

One kind of troublesome carbohydrate is the oligosaccharides [which are water soluble].... But the latest research suggests that the oligosaccharides are not the primary source of gas. The cell-wall cements generate just as much carbon dioxide and hydrogen as the oligosaccharides--and beans generally contain about twice as much of these carbohydrates as they do oligosaccharides.

Based on this research, McGee suggests:

[Soaking] does leach out most of the water-soluble oligosaccharides--but it also leaches out significant quantities of water-soluble vitamins, minerals, simple sugars, and seed-coat pigments: that is, nutrients, flavor, color, and antioxidants. That's a high price to pay. An alternative is simple prolonged cooking, which helps by eventually breaking down much of the oligosaccharides and cell-wall cements into digestible simple sugars.

In short, soaking might decrease your cooking time slightly. Otherwise, there's no good reason to do it. However, with no soaking, do be sure to rinse the beans thoroughly before cooking. I generally rinse 3-4 times with fresh water to get rid of as much dirt as possible.

It may be the case that soaking beans without salt has negligible effect. However, Cook's Illustrated has found that soaking the beans in a brine solution has a significant benefit to the beans, and all of their recent recipes using dried beans call for this step.

Here's what they have to say:

Brining isn’t just for meat. When you soak dried beans in salted
water, they cook up with softer skins. Why? It has to do with how the
sodium ions in salt interact with the cells of the bean skins. As the
beans soak, the sodium ions replace some of the calcium and magnesium
ions in the skins. Because sodium ions are more weakly charged than
calcium and magnesium ions, they allow more water to penetrate into
the skins, leading to a softer texture. During soaking, the sodium
ions will only filter partway into the beans, so their greatest effect
is on the cells in the outermost part of the beans.

Brining Formula: For 1 pound of dried beans, dissolve 3 tablespoons of
table salt in 4 quarts of cold water. Soak the beans at room
temperature for 8 to 24 hours. Drain and rinse them well before using.

They add some further explanation in their blog post on the subject:

After cooking batch after batch in the test kitchen, we now know what
works and what doesn't.

Brine Your Beans, Not Just Simply Soak, for Tender Skins

Recipes often recommend soaking beans in water overnight before
cooking. A quick-soak alternative is to bring the beans and water to a
boil and let them stand for an hour or so before cooking. Both of
these classic methods produce beans that are more evenly cooked than
starting with unsoaked beans -- and in far less time, too (in our
experience, soaking can shave 45 minutes off the cooking time).

Soaking makes for tender, creamy bean interiors, but intractable bean
skins often remain noticeably tough, regardless of the soaking time.
We discovered that soaking the beans in salt water -- in essence,
brining the beans, as we often do with meat and poultry -- tenderizes
the skins.

This works because as the beans soak in salt water, some of the sodium
ions in the water replace some of the calcium and magnesium ions in
the bean skins. The sodium ions are weaker than the ions that they
replace, so they permit water to enter into the skins, which leads to
softer texture. During soaking, the sodium ions enter only into the
skins, so the bean interiors are not affected.

First they will absorb water so the cooking will be different, if only for a reduced time.

Then, depending on the recipy you'll have more ingredients to cook with the beans which may have different cooking times (potatos for example) which can either end up raw or too cooked if the beans are in a different state.

Finally, depending on the bean the skin might end up softer or harder, giving away a different texture...

Soak (and rinse) beans to remove the phytic acid in their skins which block mineral absorption in the human body.

Either way is fine as long as the beans are washed throughly....It's just a matter of how long you want to spend cooking them...I wash/soak my black beans and then cook with a pressure cooker and the whole thing is done in an hour....and sooooo good too!!!!

I grew up on pinto beans, a staple in my life. My mother NEVER soaked the beans before cooking. Now a grandma myself I still cook beans bi-weekly. Then I read somewhere that beans MUST always be soaked first. So, I did a few times and I found that the deep bold bean flavor and color of the beans, was gone. Surely, some of the nutrients had also decreased. I was greatly disappointed! I then asked my Mexican cousin how she cooked beans. When I told her that I had heard that they must be soaked, she thought that was real silly. She definitely did not soak them. I went back to my way. I have also heard that eating beans on a regular basis will make your body used to them and there won't be a problem with gas. I also think everyone's body is different, so what works for one person may not for another. I love beans, I never get tired of them and for growing up in a poor family, they were instrumental in having good health!

I have experimented too. I think people are probably using the lazier methods of soaking, such as only overnight. If you do it right, not only do you get creamier beans but a lot less gas. I soak fire TWO days in the counter. I also keep changing the water whenever I walk past them. You will see tons of gas bubbles forming on the water, just keep changing the water. The texture is vastly improved and I can say it had pretty much removed the after eating gas issue as well.

Phytic acid needs to be removed by soaking so the nutrients are available to us. It explains this in the book Nourishing Traditions. Think about a seed. The nutrients are bound in it until optimum conditions. When they are wet for a period of time then those nutrients are unbound that the seed has them available. Then it can sprout. Traditionally all cultures soaked beans and lentils. They didn't understand why, they just did it. The newer generation want the short cuts and don't know the importance of it. Think, if we are ingesting the phytic acid (antinutrient)then we are not absorbing any nutrients. Isn't that malnourishment?

I read all the comments, and see many people have different ways they cook their beans. I experimented and soaked my white northern beans with salt, and then cooked the following day. A few days later I did NOT soak the beans and had unbelievable gas. I also noticed that when I did soak the beans that I got lots of bubbles in them when I rinsed. So I will keep soaking my beans in salt water to keep from bloating!

I know for me, cooking time is reduced when I soak overnight. I toss the 1st water, and I cook in the 2nd water. It does stop so much gas. I am only talking about Pinto beans. Other beans, I do not know.

I love my pinto beans to be a beautiful reddish color which is great for "frijoles a la charra"- bean soup. If you soak them, they become a very light brown color which is great for refried beans. So, it's a matter of how you're going to prepare the beans.

I just ate pinto beans made by someone that soaked them in cold water overnight, she rinsed them and then put them in slow cooker with 2 or 3 strips of bacon, cut in half and beef bullion. Cooked in slow cooker for 6 or 7 hours. They were excellent. My first experience, that I can remember, of beans that were not from a can. A keeper and something I would do. It was interesting reading the different opinions.

I came across this site while googling the very same question. No one has addressed a thought I had: beans (which are seeds after all) soak up moisture prior to sprouting, which changes their nutritional value. I once read somewhere that bean sprouts are veritable little nutrition bombs with a high concentration of all the good things a human needs to stay (or become) healthy.

So: perhaps soaking INcreases their nutritional value, rather than DEcrease it as someone here suggested. (I also like the idea of undigestible sugars being removed that way, and getting rid of phytic acid)

I haven't soaked beans for five years with great results. I have eliminated the gas. I've been sticking a pinhole in each bean prior to cooking. Works well, I don't notice any fragrance.