Platforms, Versions, and History of Spaced Repetition Software
Mnemosyne has been in development since 2003 and runs on Linux, Windows, and Mac OS X Leopard (Intel version). (Installation on other versions of Mac OS X is possible but difficult, and requires the ability to compile programs).
Anki has been in development for about one year and a half and runs on Linux, Windows, and Mac OS X. There is also an online version that supplments the desktop versions; however, if you have to do a lot of repetitions (say, about 300/day), the web is just too slow for normal use. Also, there is a cell phone version, but at least in Japan the cell phone data rates are so high that I would need a raise before I could do my daily repetitions on my phone (if you have an unlimited data plan, it might be worth considering).
SuperMemo has been in development for about two decades and has several different Windows versions available at different prices, along with a Palm Pilot version (made by a third party) that is not compatible with the Windows one. There is also an online version, although this is aimed primarily at institutions, not individual users. To use Japanese in SuperMemo, however, you will need either version 2004 or 2006. 2006, though the most expensive ($45), is also offers by far the best Japanese (Unicode) support, though there are still some caveats.
Since for best results you have to use spaced repetition software every day, unless you are always sure you will have an Internet connection you should use traditional software rather than a web-based application. Both Mnemosyne and Anki can be run from USB flash drives, so even if you have to use multiple computers you can do it fairly easily. Anki also has an online synchronization feature for keeping data on multiple computers in sync. When I tried this a few times (in February-March of 2008) it didn't always work, but many people are using it now without trouble.