I noticed that 干嘛 appears used in various forms of media, such as newspapers, magazines, and movie subtitles.
From a pronunciation standpoint, 嘛 and 吗 are different (neutral tone vs. second tone, respectively), but from a practical standpoint they seem to be similar.
Is there an appropriate instance to use one over the other? Or are they (generally) interchangeable?
Different sources seem to have to different opinions.
Most websites (for example http://zhidao.baidu.com/question/84845451.html and http://zhidao.baidu.com/question/219005473.html) say that the 吗 in 干吗 has a neutral tone and "干吗" has the same meaning as 干不干 (or 做不做）. For example: 咱们干吗？ (will we do it?)
According to these websites 干嘛 on the other hand means "干什么", asking why are are doing (with mostly a negative meaning). This 嘛 has second tone. An example: 你干嘛呢？ (what are you doing?)
If you however check dictionaries, you get a different answer. Of course if 吗 "干吗" as a neutral tone, it still has the meaning of 干不干. But according to these the dictionaries in the other meaning it should also be written 干吗. But with this meaning he pinyin of 干吗 is gànmá, so the ma has a second tone here. The only dictionary that has 干嘛 is MDGB, but that not a reliable one (it's one made by the Internet community and it contains many errors).
For example 现代汉语词典 has
干吗: gànmá 干什么：您干吗说这些话？ㄧ你问这件事干吗？
您干吗说这些话？ can be translated as "Why are you saying this?" and 你问这件事干吗？ as "Why are you asking this"?
现代汉语规范词典 writes
干吗 [gànmá] 1. 代 [口] 做什么 你早干吗了，现在才说 2. 代 为什么 你干吗不早说？
你早干吗了，现在才说 can be translated as "What where you busy doing before that you only say it now" and "你干吗不早说？" as "Why didn't you say before".
现代汉语规范词典 also adds 不宜写作"干嘛". In other words, you can't write it as 干嘛.
This being said, especially on the Internet you more often see 干嘛 than 干吗 and I guess in the future both will be probably become accepted forms.
Put it in simple way,
干嘛 means what's up or what did you want?
干吗 doesn't make sense in Chinese, what makes sense is to be used in a context. i.e. We're gonna RUB the bank(kidding), 干吗 (wanna do it)?
The tone is important when talking about the difference between "干吗" and "干嘛".
There is no problem if you always use "干吗" when writing. (of course you are talking about writing, or someone wrote and you are reading). This is because the reader can understand "吗" is a neutral tone or second tone, depending on the context.
"干嘛" is always second tone. So potentially it can save the reader 0.01 second of determining whether it should be a neutral tone or second tone.
As to what neutral tone or second tone means, I quote BertR's great post.
IMHO, "干嘛" is becoming popular recently because:
In the old days, I would save considerable time to use 吗 instead of 嘛 if I have to do hand writing.
As a consequence, "干嘛" beat "干吗" if the tone is second.
干嘛 does not equal 干吗 嘛 is colloquial for 什么 干嘛 = 干什么。So 你在干嘛 = 你在干什么 = What are you doing?
干吗 = 干，吗？Doing it？ 你在干吗 = Real Chinese people will understand it as, Are you copulating right now?
