If a graph is posted to a website, you shouldn't need to ask permission because it is publicly published. Simply cite the source webpage following the convention of your publisher.

It is not always that simple since the question of what constitutes "Fair use" is not clearly delineated. If being used for class notes then it could be argued that since it is neither being "openly" republished nor for obvious financial gain that it is covered by "fair-use" policy (provided it is properly referenced). If however, your work is to be publicly accessible (e.g. published to an open-source repository) then it is most advisable to request permission. This is usually merely a matter of clicking an embedded link within the webpages and outlining the pertinent details of your intended use.

Even such action is considered excessive, it serves two positive purposes:

1: It is courteous.

2: It presents one as "walking the talk" - We constantly insist that our students:

     - provide proper referencing

     - avoid plagiarism

     - avoid copyright infringement

We therefore should try to be beyond reproach as far as possible.

P.S: When contacting a web administrator for permission it is a good idea to include an addendum such as "A non-response will be taken as agreement" since some site administrators do not reply.

I think it's not the same as citing something, where you can just say "he said that" (he, year).

I would explain the reason that you want to use their graph rather than create it yourself. Perhaps, they did not make the underlying data available, so you want to at least use their graph. Or maybe their graph is oh so amazing and it responds to precisely what you need, so can you please just copy it and say "source: ...".

A few times I have wanted to make direct use of images for a project. I feel different about taking an image than citing an idea or factoid. I contact them, explain the project in general, explain the specific reason that I want to use their image instead of creating it myself or using some other source. They probably they will say you can use it, but only for the specified purpose. For example, one time I was looking for a map of a specific subset of countries, and instead of buying and learning how to use some special map software (which I didn't have the time or budget for), I requested to use a third party image located online from a company which I new to be reputable in a relevant area of activity.

As to your specific question: no, I would not have felt right to use that image if they had not responded, but it was a private company, not an NGO or IO. Probably I would feel OK with Phil's suggestion for most NGOs and would feel free to make direct use of UN or government sources which are attributable directly to the organ/ministry/level of government (and not to some authors or firm which may hold IP rights over the image) as long as there is a citation with sufficient information for a reader to corroborate the information and/or replicate the process.