"Labels" in Gmail. Gmail users love 'em, Outlook users hate 'em, at least at first.
The great thing about labels is you can use them exactly like folders, but why would you want to? Labels are much more flexible and offer some distinct advantages to the antiquated notion of folders.
The problem with folders in computer applications is that they were built to mimic a file folder in the real world, including all of the limitations inherent in that system. With folders you have to compromise between meaningful categorization (thus ease of access) and ease of maintenance. Imagine printing all of your emails and slapping them into manila folders1 labelled "project x" "important" and "financial." What the heck would you do with an email with a large invoice for Project X? Surely you don't want the hassle of keeping up with three copies of the same email? But that's what you are facing when you limit yourself to folders in a traditional email system.
1If you don't know what a manila folder is you probably don't need to be reading this anyway.
But if you really want to, you can stick with a one-label-per-email scheme and it will work just like folders, but I don't recommend it.
The section titled "Understanding Labels" in this training video gives all the details you'll need to move into the "love 'em" column.