For vocabulary, obviously a dictionary would be the best thing, but for specific vocab then perhaps you could study those covered by the Japanese Language Proficiency Test. In which case, this site is good for testing the vocabulary that appears in each level of the test - http://jlpt.renshuu.org/
For Kanji, again, I can't really say much beyond dictionaries. Jim Breen's Online dictionary has a kanji search feature. http://www.csse.monash.edu.au/~jwb/wwwjdic.html
For grammar, I know a few good sites:
http://www.tanos.co.uk/jlpt/ - List of all JLPT grammar (also vocab & kanji)
http://www.nihongoresources.com/ - A bit of everything
http://www.guidetojapanese.org/index.html - Lots of grammar explained in easy to understand English.
http://www.jgram.org/ - Lots of grammar, including JLPT grammar.
http://www.nihongo2.com/dictionary/index.cgi - Heaps of grammar patterns but all explanations in Japanese.
For general internet use, there are sites like http://www.rikai.com and http://language.tiu.ac.jp/index_e.html which process web pages and show you the readings for the kanji as well as their meanings.
If you use Firefox, there's a plugin called Moji that lets you highlight text and find the meanings of words and kanji. You can find that here: http://moji.mozdev.org/
http://www.japanese-kanji.com/
http://www.kanjisite.com/
http://www.aiu.ac.jp/~kawatsu/gahoh/English.html?PHPSESSID=17bad0deef453cf714b01b718a1944c3
(This last one helped me to understand the "combined-Kanji"-characters better)
http://www.manythings.org/japanese/ (for instance http://www.manythings.org/fq/m/2997.html )
http://www.csse.monash.edu.au/~jwb/wwwjdic.html (it was mentioned before, but I like to highlight this feature: http://www.csse.monash.edu.au/~jwb/wwwbuttongen.html (I use these all the time)
And this might be useful too (it's a plugin for firefox, I am not sure, if it's the same as mentioned before...): http://www.polarcloud.com/rikaichan
And for some starters lessons on Japanese vocabulary and grammar: http://www.japanese-online.com
- Rikaichan, Firefox / Thunderbird translation plugin
http://www.polarcloud.com/rikaichan/
Allows you to highlight and translate words in web pages and emails. My #1 tool for surviving at work!
- http://www.alc.co.jp/
Fantastic for not only finding direct word translations, but also seeing them used in the content of a sentence. Works particularly well in conjunction with Rikaichan.
- Kanji Sonomama Rakubiki Jiten (Nintendo DS)
http://tinyurl.com/2h4dvx (goes to amazon.co.jp)
This is Nintendo DS software rather than an online resource, but it's too useful to ignore. Allows you to input kanji using a touch-pen for translating signs, or just to use as a dictionary while reading books or comics on the train. Also good writing practice!
Beyond what has been suggested here are a few more sites.
The first 3 are related to the Genki text books but are good even without them. The third being audio lessons (good for listening comprehension). And the fourth being other vocab based off of other text books.