The first add-on I got recommended to me by my teacher was Perapera-kun. It is an add-on that shows you translations when you hover over a kanji in a text. At that time I was using firefox as a browser which was well supported by Perapera-kun at that time.
But the I switched browser to Chrome and lost access to Perapera-kun. Since I was addicted to the functionality I dug around a bit and found Rikaikun which provided the same functionality and worked with Chrome. Apparently Rikaikun is based on an firefox extension called Rikaichan so if you use firefox you might try that one too.
It looks like the people behind Perapera-kun is working on a Chrome version but they seem to go for the Chinese version first so no telling when it might be available for Chrome.
I don’t use Safari, Opera and Internet Explorer enough to know what extensions there are currently available for those browsers.