Shinobi III has been released on several systems, here is a list of them all.
IPHONE
An iPhone version of Shinobi III was released in 2011. I've never played it, but it seems to have everything from the original game along with a save option. And, from all the reviews I've read, horrible controls, with touch screen buttons which take up a great amount of space. There is a way to change it so the buttons don't overlap, but this makes the screen smaller.
MEGA PLAY
SEGA's Mega Play was an arcade system and the follow up to the Mega-Tech. Mega Play allowed players to choose from one of several Genesis games and play it. This is another version I've never played, but from what I've read, each game was changed slightly compared to the original Genesis version, such as removing any extra life items. The flyer used for the Mega Play features images from a prototype version of the game, as seen by the HUD and speeder bikes in the second screen -the images could be from this prototype. For more information about the Mega Play, visit SEGA Retro.
PC
This version is available to download on Steam, but if you'd prefer to have it on a physical disc, it is included on the SEGA Mega Drive Classic Collection Vol 1 and the Gold Edition of the collections.
PLAYSTATION 2
Shinobi III is one of many games in this 2006 collection.
PLAYSTATION 3
This 2009 collection features Shinobi III along with many other Genesis and a few arcade games. There is a trophy you can unlock in Shinobi III called "True Ninja Skills" which is very easy to get -you just need to complete the first round without using any continues.
PLAYSTATION PORTABLE
This collection, which features the same content as the Playstation 2 version, was released in 2006.
WII
The Wii version is available to download for the Virtual Console, and it costs 800 points.
XBOX 360
This collection, which was also released for the Playstation 3, features Shinobi III. An achievement can be unlocked in Shinobi III called "True Ninja Skills", and like in the PS3 version, you just need to complete the first round without using any continues to get it.