How can voice be classified based on range? What system is typically used? Which voice types are there? What are their ranges? Are there other less-known or alternative systems?
That's a pretty broad question. This Wikipedia page covers a lot of the issues involved, and it definitely agrees with my experience: http://en.wikipedia.org/wiki/Voice_type
The most common classification is simply soprano and alto for women's voices and tenor and bass for men's, but as you'll see in the article that may be the most common division composers use and cite in their music, but it doesn't cover the terminology professional singers and coaches use. Range is only one aspect of vocal style that goes into vocal types. For example, a coloratura soprano generally has a much higher range than a dramatic soprano, but the former term also refers to the specific kinds of fast arpeggiating figures they focus on and the latter term implies greater vocal weight and volume.
As you say in your comments @JCPedroza, there is a well recognised classification system based upon range of male and female voices. And @Pat Muchmore's point about different vocal styles of vocalists, within each of these ranges, allowing another level of classification, is a good one.
I only wanted to add one main idea, that of classification by vocal production, in particular with regard to the male countertenor voice. Not only is this a distinct range of voice, but also distinct from other male voices in terms of vocal production; modern countertenors generally use falsetto for the upper part of their range. Other male voices will use their modal voice, as most countertenors do for the lower part of their range. However, there is further classification by vocal production within male singers singing within this range too, as the castrato voice is (or should I say, generally, was!) able to sing within this range without the use of falsetto (as too, of course, are unbroken male voices).
As an aside, while reading up on the ideas above I spotted some links that may interest you: