GW-BASICWhen I first learned BASIC, there were two types of computers at my school. There were computers running Microsoft DOS and there were Apple computers (I believe Apple II series). I learned to use both and program on both. They really were not that different. The first I heard of Windows was when the teacher ("King Draper" or Mr. Draper to lesser mortals) found that kids were bringing in copies of Windows on floppies. Windows was okay after school, but was not appropriate for class.
In that time before Windows, there were many versions of BASIC and every kid learned how to code with at least one of them. Representing this period of time is GW-BASIC. So many old programs and games were written in or rewritten in GW-BASIC that it is still easy to find thousands of GW-BASIC programs floating around online.
If you have a 32-bit Windows or DOS computer, you can download and use the original GW-BASIC. If you start at the Wikipedia page for GW-BASIC (https://en.wikipedia.org/wiki/GW-BASIC), you can follow the links in the links section to download the interpreter and find tons of information and programs written in BASIC.
Vintage BASIC is a GW-BASIC compatible interpreter written in Haskel. Find it at http://www.vintage-basic.net/
PC-BASIC is a GW-BASIC interpreter written in Python. It will also run BASICA and a couple other varieties of BASIC. Find it at http://robhagemans.github.io/pcbasic/
QB64QB64 is meant to be compatible with QuickBASIC, but is really its own language. But what QB64 lacks in compatibility with QB45, it makes up for in other ways. First, it runs on newer computers. Second, it has more modern features that make it more suitable for graphics programming on current computers. It is also possible to program your android devices using QB64! There's something you can't do with QB45.
Check it out at http://www.qb64.net/
FreeBASICLike QB64, FreeBASIC is supposed to be highly compatible with QB45 code. When testing, though, I found quite a bit of QB45 code that would not work. This has not stopped people from creating some great games and applications using FreeBASIC.
Find FreeBASIC at http://www.freebasic.net/
BlitzBasicBlitzBasic was the original interpreter for a BASIC dialect. Now, although the website (http://www.blitzbasic.com/) is still called BlitzBasic, the original product is gone. The influence of BASIC is still there, though. BlitzPlus and Blitz3D are now free and open source!
DarkBASICDarkBASIC is another BASIC designed to help people make video games quickly. The creators of DarkBASIC now have many more products to choose from including DarkBASIC Professional which allows the quick creation of 3D games using DirectX. Check out DarkBASIC at http://www.thegamecreators.com/?m=view_product&id=2030
Monkey XFrom the people who brought you DarkBASIC, comes Monkey X. Monkey is based on BASIC and is designed to help people create games for multiple platforms. I have not used Monkey X, but it does look cool.