Yes, there's a standard Japanese test which has levels 1 to 5, called JLPT. 1 is the highest and 5 lowest, I was able to pass level 2. It's sort of exponential though, you need to know twice as much for each next level basically.
I seem to recall that Japanese Universities require level 3 for exchange students to enroll in Japanese language classes. That's probably not enough to follow lectures, but probably enough to get to the level of being able to follow lectures after 3-6 months.
My literacy is pretty poor, so I don't think I'd be able to pass a level 3 test, but I think apart from the literacy part it's probably a decent description of my current level.
Coming from latin-alphabet languages, it takes some effort to get up to speed -- the primary school curriculum is 1006[1] kanji characters, along with 2*48[2] (depending of how one counts) kana. And that's just the bare minimum, general literacy is ~3000 kanji.
It's a fascinating language, and learning it gives some interesting linguistic perspectives because it's so different, especially from other big languages. It's also a rather simple language -- the main difficulty lies in how different Japanese is, due to the long isolation.
