You can go to the official page to play the free browser version of Wolfenstein 3D here. The game weirdly enough also supports a mouse control feature (but come on... play it right the way!) and also lets you select from all the original levels right off the bat.
In addition, Bethesda also released a special video online of John Carmack (the creator of Wolfenstien, and Id Software's Co-founder) playing through the first couple of levels of the game while providing commentary and insight. In the video, Carmack is playing the DOS version of the game however, he goes into details regarding the game's many ports including the SNES, Jagguar, and IOS version. Among other things, Carmack also discusses the game's technical aspects, bugs, and as well as how the game's mod community also helped develop the IOS version.