Save States for older game consoles?
There's not a hardware device that would sit between a console and it's cartridge to record the game's state, and that's because it wouldn't be able to do this task.
The cartridges hold the game's code, commonly burned into memory chips called ROMs. Cheat devices like the Game Genie or Action Replay sit between the console and these chips, and replace or patch the code on the chip as the console requests it. Therefore, it's possible to change the way the game executes in real time.
For example, when you get hit in The Legend of Zelda, there's a bit of code that executes which takes your current life (stored in a memory cell) and subtracts one from it. Instead of subtracting one heart, the cheat device might change the code so that the "subtract one from life" instruction is never executed. This would make you effectively invincible.
Saving state is done by copying the current contents of memory/registers into a file, and then loading that file again later. The console's memory is not part of the cartridge. Therefore, this can't be done by capturing the data coming off the cartridge - you'd have to open the case, and solder down something that is capable of reading the contents of the console's memory, and allow it to be restored later. This is a complicated process, and would likely be hard to get right.
Saving state is a common feature of emulators, however. Emulators set up an environment inside your PC where the entire CPU, memory, audio/video chips, etc are all simulated. Since they're simulated, capturing data at any point in the process is fairly simple. Older generation consoles had a tiny amount of memory compared to your PC, so saving and loading many different iterations of the current game state is simple and not very taxing.
Forgive my bluntness but Agent86 is not entirely correct.
Both the SNES and NES actually do have hardware devices that can save and restore state with off the shelf cartridges. As an added bonus both offer true slow motion capabilities (not the pause button hack commonly implemented by some controllers). These are perfect for games like Mortal Kombat and Battletoads.
For SNES you are looking for the Nakitek Game Saver Plus available at www.stoneagegamer.com for about 20 bucks.
A Genesis version was mentioned in a Game Pro magazine back in the day http://www.digitpress.com/forum/showthread.php?91593-naki-game-saver
But the Genesis version they talked about never saw the light of day.
For NES you want the much more rare and elusive Game Action Replay (not to be confused with the Pro Action Replay, a game genie like device.) these are very hard to find and typically go for 80-100 dollars on ebay.
I own both and they work mostly as advertised with a few quirks. Because of the lack of accurate information and abundance of misinformation on these devices I am in the process of putting together a complete review.
I should be done with it sometime in February and I'll post a follow up comment with a link once it's up.
In the meantime order it now if you want it because once I clear up the confusion that's currently making people overlook these devices they are going to become very hard to find!
Actually, the PowerPak -- basically a flash cart for the NES -- does have the ability to take savestates, with a certain set of mappers: http://kkfos.aspekt.fi/projects/nes/powerpak/save-state-mappers/
It is not currently possible for the other ones, that I know of, however.