As I've made it clear in interactions with certain websites, I don't believe there is one form of minimalism. Heck, the word itself is sort of a nebulous term, not really saying anything aside from the emotional connections a person might attach to it themselves.
So here are terms that I would associate with my form of minimalism.
I've probably already made this part of my opinion dreadfully clear, but I don't like to buy things. I think this comes from working two retail jobs. Eventually you start to become disillusioned with the field, to the point of repulsion.
By this I mean, when I find something that interests me, I focus deeply on it. I eliminate things in my life that separate me from my focus, either permenantly or temporarily.
For example, I do enjoy the occasional video game. Perhaps in the future I will shed it as a hobby, but for now I enjoy it as long as the game in question is engaging enough that I have to work my mind to solve its puzzle. Action games such as SOCOM or simulation games like Persona allow my mind to create elaborate strategies to solve difficult situations.
Once I stopped buying video games (anti-consumerism) I was able to focus more carefully on the games that interested and stimulated my mind the most. I enjoyed games much more after I applied focus than before.
I extend this example to all points in my life, from work to books to friends and objects in my room. Quality over quantity.
I have mentioned this in a computer aspect and it can extend elsewhere.
Basically, I never lock myself into anything. In an ideal sense, I would be able to flow like water out of any situation or mindset if needed.
Wikipedia describes simplicity as:
"Something which is easy to understand or explain is simple, in contrast to something complicated. In some uses, simplicity can be used to imply beauty, purity or clarity."
On that note, something simple should be easy to understand. Therefore, if I consider it minimalist, I consider understanding fundamental.
Too often I see evidence of people who only care for a process' output, not the process itself. To that I argue, how can you fully understand the output? There is nothing without an origin.
Here are some minimalist ideals that I have seen before but reject. I do not attack the author, only the idea.
As much as I like unadorned or featureless art and design, I don't consider it a priority and will not going out of my way to make sure that I have it.
Basically, the way I see it is that if you have to use a toolbox, it doesn't matter if the toolbox is white and shiny or gray and blocky. What matters more are the tools inside. For me, if I were to use a white and shiny toolbox, it would have the exact same tools that my gray and blocky toolbox would have. So while it would be a prettier toolbox, it would not be functionally more powerful.
I value functional minimalism over aesthetic minimalism. It would be better to make the tools inside more powerful, easier to wield, and tailored to the user that is using them rather than just make them visually appealing or aethetically stripped clean of excess. Often this can help functionality, but not always.
While removing objects from your house/computer/mind is often a good way to increase focus, it is not the nature of miniamlism for me nor is it a pillar of my ideals.
Subtraction is merely a means to get to focus, but it is not focus itself. It's not enough to say, "Oh, look at my desk, I have no papers on it now." You need to put that desk to good use and better use after it has been cleaned to really make your focusing work.
I am wary of websites that say that having less items in your home is a way to help you achieve minimalism, because while that may be helpful to some people, for others that is not what they consider minimalist at all.
Additionally, a stigma against minimalism is that it is subtraction simply for the sake of subtraction, which is wrong on several levels.