Another superb Nemesis remake with a normal single player and online modes added along with some user created extra stages called Nemesis online,
no install required and available for download here :- Nemesis Online
I think you'll find there were games and clones of those games on all formats, the amiga in particular had loads of clones of those games released in the public domain.
The original versions of boulderdash and dig dug at least had their roots way back in the early 80's and both were released commercially on the commodore 64 later in 1984 and 1983 respectively (considering not all systems have their own thread) i suppose the commodore 64 one is where any remakes will end up being posted.
Ok to start off here's a nice remake of boulderdash no install required and available
Here's a remake of the original c64 version of tetris by mirrorsoft, it doesn't seem to have been enhanced in any way, but that also means you won't need an emulator and it comes complete with that tune
No install required, enjoy a classic before nintendo gobbled up the rights to it.