I think a big part of it is reducing visual noise. The less “Stuff” there is on the screen, the less complicated the program feels, and users’ sense of confidence in their ability to grasp the software increases. This was as true in the 90’s as it is today, but the reason you’re noticing it now is that we are starting to re-evaluate our assumptions about which UI elements are necessary and which are just training wheels which we as users outgrown.

A classic example is visual borders. Visual borders were used much more extensively in the past than they are used today. In the 90s they served the purpose of spelling out to users how information is organized. While grouping items together creates a sense of organization in itself, the convention that grouping is most likely intentional is not necessarily a conclusion you’ll jump to. It’s something you need to arrive to by examining the screen for signs that confirm this suspicion, and that’s effort. Visual borders were used to reaffirm that the groupings are intentional, and to emphasize the apparent structure of the program. Nowadays we’ve mostly outgrown visual borders as necessary training wheels; people will readily assume the grouping is intentional and meaningful, and will even expect it. In fact, people don’t even need pressable items to look pressable, they can infer from context that this text/flat box can be clicked on to have effect. You may be asking yourself “but does the button have to be flat?”, and the answer is that if you want to maximize visual simplicity: it does. A plain blue rectangle over white background is one change from blue to white. A plain blue rectangle surrounded by a black border, placed over white background is two changes: from blue to black and to white. Add shadows, and you get a third change.

I also believe that developers are starting to assume less expertise on the user’s part. For example, a typical rationalization for not putting in yet another button on the interface is that we ask ourselves “will this be something the user will have to actively ignore 90% of the time?”. If that’s the case, then the user’s ability to find the button they do need is reduced, because it’s hidden in a bigger collection of buttons. In the 90’s the average developer would probably think “well, once the user does know where their button is, this problem disappears. They do not need to search for it anymore”, and this is a point of view that assumes the user can be expected to rise up to some standard of familiarity with the program. Nowadays we prefer not to assume this. We prefer to create software that will also be usable by the most clueless user possible, that sees the program for the first time, or even sees a program for the first time. This is definitely a business-oriented constraint. We live in a world where high end technology is being targeted at mainstream markets. It’s not a niche anymore, it’s not only aimed towards high earners or hobbyists. A $400 iPhone can be a present to your grandma. She should be able to figure it out, and if you care about her figuring it out, you should pay attention to the trend.

Your feelings of dissonance are understandable but not warranted. Simplicity and function are not necessarily mutually exclusive. Stack Overflow is simple compared to the UI cacophonies that many news sites are, but it’s also useful. The iPod when it came out was simpler in terms of hardware buttons than other players, but it was just as capable. The average smartphone app has less buttons at any screen than old Symbian phones had (before the advent of touch screens), yet they are easier to use and more capable. In short, there’s a difference between function and design. They’re not strongly coupled (perhaps loosely coupled, but not strongly). When you understand that, most reservations about the simplification of UIs go away. It’s a paradigm shift, not a step back.

It’s for simplicity’s sake, and no, you do not have to follow that trend.

I suggest that you do conduct your own usability tests and work from there.

Fancy interfaces tend to start looking extremely cluttered very quickly. Interfaces that require a lot of components must be plain for that reason. Were those buttons all to have flashy bling effects on rolling over them, textured edges with frilly gold trim, maybe even sound effects (and yes, I’ve seen all that and more) the application becomes impossible to use productively.
And productivity is what most applications (including most websites) are all about. Not everything is a game, get used to it. I don’t want a cluttered, fancy looking, user interface. I want something that’s instantly and intuitively useful to me, where my eye is guided to the most common components simply by their size and placement, where the rest is tugged away where it’s easy to find yet does not intrude on my more common tasks.
Hence Google with its simple layout of an input box with 2 large buttons underneath. And hence the light grey colour of the comment and tag links here (among other things).

I’d like to bring the opinion that I heard from a professor at the university I study in and from my sister who is a graphic designer (surprisingly they had the same opinion though their professions have very little in common).

They say that the plainer the interface is, the harder is to make it look good. With the shiny and volume stuff that Windows 7 has, it is very easy to make things look “cool” without any much effort. This means that it doesn’t matter if you are a professional or an amateur _ your application has a big chance to look good. You could compare this with drawing with pencils and with felt pen.

Besides, plain applications look more simple and intuitive, which is very important since no one likes to read big instructions in order to be able to use an application.