I passed level 2 of the Japanese Language Proficiency Test without studying kanji systematically. But I realized that I would have to use a system to tackle level 1.
There are just too many kanji to try to acquire them naturally. After looking at every book I could find, I decided that the Japan Times "Kanji in Context" had the most advantages. I especially liked how the kanji are arranged roughly by theme & relative frequency of appearance in newspapers, not just according to the Education Ministy's list of progression.
The kanji for monkey, for instance, is known to every 8 year old Japanese kid, but unless you're visiting Nikko you won't have much cause to use it. So although it is relatively ear the top of the Education Ministry's list, you'll almost never see it in the newspapers unless it's an article about visiting Nikko. So "Kanji in Context" includes it at the very bottom of their list.
The "Kanji in Context" system divides the Joyo kanji into 6 levels. The first 2 levels are the beginning kanji, which roughly correspond to the kanji you'll encounter in level 3 of the JLPT. Actually, since these are the most common and basic of all the kanji, you'll encouter them all the time everywhere Japanese is written. You must master them.
Levels 3-4 of "Kanji in Context" go beyond the kanji which are on level 2 of the JLPT, and could be described as "intermediate" and "intermediate-plus". These are the ones which will drive you mad, because they include many of the common abstract kanji which appear in newspapers and magazines. Level 3 is the real bear -- a total of 850 kanji, and that is the list I've compiled. Level 4 is shorter (220 kanji), and these kanji are not quite as common as the level 3 kanji.
Level 5-6 are the kanji with very specific meanings and limited uses. It's pretty pointless to memorize them because you won't see often. Instead, just pick them up as they come your way.
So about the time I was finishing working my way through level 3, I discovered Stackz, tried it out, and thought it was pretty cool. After using it to compile the level 3 list from "Kanji in Context" I can confirm for you that it is very cool, and that it really lends itself to studying kanji. The advantage is that it allows you great flexibility in designing a ystem to study the kanji you want to study.
Good luck to all.