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Does this sentence (the part in bold in particular) sound natural?
When I hear a siren, I always become so curious that I cannot help running to see what is going on there.
Comments  
Natural, yes. Delete "there" from the end of it though. It seems redundant to me.
It sounds natural enough to me.
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If I said it, it would be can't help, but other than that, it sounds fine to me.
CJ
OK, thanks everyone.
Now, would you come up with any verbs which you think would sound strange if used with 'can't help'? If it sounded strange, then why?
I don't think there are any restrictions regarding the verb, but the subject should probably be animate. For example, the following, though grammatical, is very strange:
The concert can't help lasting two hours.
Emotion: smile
Do you have any potential candidates for the class of verbs you're looking for?
CJ
Students: Are you brave enough to let our tutors analyse your pronunciation?
CalifJimI
Do you have any potential candidates for the class of verbs you're looking for?
CJ 

No. And that 'cannot help running' wasn't a candidate until I found a book (written by a Japanese) which said it didn't sound OK; it said it had to be 'cannot resist running' instead, but I thought it was almost the same.
resist is a higher register word than help in that context, but other than that, I see no difference.
CJ