The verb わかる can be written using either 分かる, 判る, or 解る - what's the semantic difference between these forms, if any?
The answer lies in the kanji. This data is from EDICT/Jim Breen's kanji lookup:
分かる is clearly the most common - just to know or understand something:
解る implies understanding of a problem, not simple knowledge.
Which implies to me that you solved the problem. If I read the same sentence with 分かりました, I might not think twice -- but it could also mean that you didn't spend any time solving it at all; you already knew how to solve it (and therefore did so immediately).
判る is probably the least common use I've seen in the wild.
Because the word "judgement" is connected to it, ala 判断 (はんだん), so if a judgement was made that something WAS something, that might be 判る. A cursory Google search yielded this Yahoo! page which indicated the same.
DISCLAIMER: These sentences and translations are my own, and I'm no translator, nor a native speaker!
First, before getting into the semantic difference, it's worth noting that 分かる is rarely written with the two alternate kanji you listed. The general consensus (after searching through several Japanese Q&A sites, since this is a question that native Japanese have about their own language) is that 分かる is universal enough to cover all situations. (And if you're not sure, you can always resort to わかる, which is perfectly acceptable.)
This said, the difference can be summed up as follows:
As you can see, there's some overlap between 分かる and 解る, and depending on the context you could substitute them for each other. But while most people may be able to read all three versions, the safe choice is to stick with 分かる unless you have a good reason not to.