As mentioned by someone else, QBasic is still around, and there's also Gambas (which is as close to old-school VB as one can get on Linux) if you're looking to play with something.
MS Basic kiiinda became as close to a defacto standard as can be described, just because it was the most common and commonly imitated.
In terms of a modern standard, there's quite a few modern BASICs, but the same kind of applies: Microsoft kinda leads the field. Many of the surviving projects are either directly or indirectly based off of QuickBasic and Visual Basic, or at least heavily inspired by them.
* FreeBASIC
* QBasic64 (an unofficial continuation of MS QBasic)
There is of course also VBScript / VBA and VB.NET but I think it's a bit a stretch to put them in the same bracket (particularly with VB.NET). It is a little like calling C# a dialect of C.
In terms of experience though it's nothing like the basic on these machines. Shell scripting with curses is probably the closest modern equivalent.
That leads to the obvious question whether there are there more modernized BASICs out there now. Is there a standardized ES6 equivalent, perhaps? ;)