Note: This is an AmE perspective (BrE is different, see comments/other answers)

*Crowd* is singular.  *Crowds* is plural.  You can't use *crowd* plurally, you have to use *crowds* if you mean more than one crowd.

Verbs work the opposite of nouns, verbs that end in *s* or *es* are singular third person and verbs that don't are plural third person.  (Anything not third person uses the form without the *s* or *es*).  

So it's always *crowd believes* and *crowds believe*.

Nouns that describe a group of X as a whole are singluar, if they refer to one of that group.  If there are multiple groups of X, then plural is used.

> I don't know where the pile of papers is (*pile* is singular because it refers to *one* group of paper)

> I don't know where the piles of papers are (there are two or more stacks of paper)

I think it's technically wrong, but you might hear something like this where a plural pronoun is used.  I'm not sure whether referring to a virtual "all of the papers" which can be argued to be implied is totally wrong here.

> I took that pile of papers and threw them in the trash.