Cause for vs cause of

This ngram would suggest that cause for is not as frequently used as "cause of". "Cause for" seems to mean "a valid reason for", as in "cause for alarm". "Cause of" implies a causal relationship, as in "this is the cause of that".

I personally can't think of many contexts where "cause for" would be appropriate other that "cause for alarm" and phrases similar to it. As Daniel says, similar phrases are "cause for concern", "cause for panic", etc

Prepositions don’t necessarily translate one for one. It’s the problem’s cause, no matter which way you look at it.

Consider Latin casus belli. That might be translated at war’s case or case for war. Notice it is not case ∗of war.

Sometimes the English word for looks towards the future, and sometimes it looks towards the past. Here:

Ya ain’t got no cause for complainin’.

It’s looking towards the future, and is equivalent to cause to complain or cause for complaint.

But sometimes English for looks towards the past.

There’s gotta be a cause for this mess. This crap doesn’t happen by accident.

In that situation, for is looking in the past, and could be replaced with behind.

Other forward-looking examples of for include:

This present is for John.
This card is for taking out money from a bank.

Other backward-looking examples of for include:

I did it for my children.
I got four quarters for a dollar.

You have to translate by sense, not by exact word. Not all languages support a for preposition that has so many different senses as English does. Two such examples are Spanish and Portuguese, where you must always figure whether in any given phrase, for=por or for=para.

To my mind, cause for is only felicitous with positive outcomes:

His arrival was the cause for much rejoicing, great joy, unbridled celebration, ...

As opposed to:

His arrival was the cause for much handwringing, great panic, unbridled flight, ...

— all of which sound slightly odd and are improved, I feel, by use of of:

His arrival was the cause of much handwringing, great panic, unbridled flight.

That said, I’m not aware of much prescriptivist ink being spilled on this topic, so others may have a different impression of what constitutes standard usage.