Is there a table like this for Chinese characters, that lists which Chinese characters are taught for each year of primary school?
(I'd like to learn Chinese, so this would be a great source of information about what characters to learn first.)
This list roughly groups the 5568 most common characters over the nine years of compulsory education in Taiwan. You didn't specify if you were looking for simplified or traditional, but since I only know of this one source and it's traditional, that's what I will recommend.
It should be noted that this isn't an official list of what pupils should learn, but rather the result of doing some statistics on textbooks and reading materials. I don't know what you want to use the list for, but as a learner of Chinese, the first seven levels are definitely useful and probably the eighth as well. The ninth level contains a lot of proper names and characters that aren't all that useful in my opinion.
Update March, 2020: The original web page is no longer reachable, so I have replaced the link to an archive copy over at Wayback Machine. This is the original link, which no longer works.
This (simplified Chinese) table with Pinyin might be what you want.