Question: I know ため can be translated into English as "for" such-and-such.

But is it appropriate to use it to thank some one for doing something? 

For example, "Thank you for your email address." Would it be grammatically accurate to say: メールアドレスためありがとうございます。

Google translate seems to understand the sentence perfectly fine. But would a native speaker scratch their head at that use of ため in this manner?

Answer: 
Using ため as the 'for' in 'thank you for' is strange.

Off the top of my head I can think of 4 ways we normally use ありがとう to say thanks for something.

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> 1. masu-stem of the verb + ありがとう (this one's particularly formal)  
> 
>  メールアドレスを教えていただき有難う御座います。  
> 
>  Thank you for telling me your email address.
> 2. te-form of the verb + ありがとう  
> 
>  メールアドレスを教えてくれてありがとう。  
> 
>  Thanks for telling me your email address.
> 3. noun + ありがとう  
> 
>  メアドありがとう！  
> 
>  Thanks for your email address!
> 4. [noun + を + ありがとう](https://japanese.stackexchange.com/q/5496/78)  
> 
>  メッセージをありがとう  
> 
>  Thanks for your message
> 
> 
> 

There's lots of other expressions which don't use ありがとう like:  

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> ～についてお礼を申し上げます  
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>  ～に対し感謝します
> 
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> 

ため is 'for' as in for the benefit or purpose of someone/something.  

> 
> `私のために`こんなすてきなパーティーを開いてくれてありがとう。  
> 
>  Thank you for throwing such a splendid party `for me`.
> 
> 
>
It might be easier to understand the usage if you think of `ため` as "for the sake of (smb/smth)".

> 
> 会社{かいしゃ}の**ため**に働{はたら}く  
> 
>  Work **in interests** of the company [=for the sake of the company] 
> 
> 
> 彼女{かのじょ}は娘{むすめ}の**ため**なら何でもやる  
> 
>  She will do anything **for** her daughter. [=for the sake of her daughter]
> 
> 
> 正義{せいぎ}の**ため**に  
> 
> **In the cause of** justice [=for the sake of justice]
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> 

A related meaning is "for the purpose of" or "with the goal of"

> 
> 君{きみ}は何の**ため**にここへ来{き}たのだ。  
> 
> **What** have you come here **for**? [=for what purpose] 
> 
> 
> 金{かね}の**ため**に働{はたら}く  
> 
>  Work **for** the money [= with the goal of getting money]
> 
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> 

`ため` may also means "due to" or "because of". It seems to be used this way mostly in formal speech. You can often recognize it by the missing `に` (but this it not a 100% indicator).

> 
> 飛行機{ひこうき}が台風{たいふう}の**ため**欠航{けっこう}した。  
> 
>  The flight was canceled **due to** a typhoon.
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