My field is international business and I've co-operated several times with other people without special funding for all participants: written some articles, co-edited 2 books.... Of course, such co-operation may fail, too, if you don't have project financing to push you to finish it, but it can also succeed.
Funding of some sort is usually necessary for all research. Unfunded collaborations usually sink before they start. Books, journals, visits, conferences, computers, other equipment, materials, offices, labs or field work all need money, and any staff involved needs to be paid.
My field is international business and I've co-operated several times with other people without special funding for all participants: written some articles, co-edited 2 books.... Of course, such co-operation may fail, too, if you don't have project financing to push you to finish it, but it can also succeed.
Thank you all Ian, Alan, Larisa, and Tiaa for your valuable answers and elaborations. Unfunded collaborations seem now easy to start, depending on the "network", but hard to maintain and hard to predict their outcomes (and the qualities of the outcomes) - if not hard to succeed. I think they are highly worth involving in, as frequently as are in the funded ones, as a lot can be learnt from, cheaply.
In France, where researchers or teachers get already their salaries for doing research, it is a rather usual thing to have unfounded projects (or projects for which no specific budgets are forseen). Those research projects are an intrinsic part of the activities of a research lab and which are budgeted (this is the case of public research labs). However more and more researchers and research labs compete on a national or international level in project calls (in France, habitually launched by the ANR - Agence National de la Recherche) in order to finance specific R&D projects or again R&D projects that require an extra-investment.
I have quite good expierience with conducting international research without funds. Naturally, it is possible in social sciences (esp. cross-cultural psychology), where no expensive tools/aparature are demanded. In our project finally participated scientists from 28 countries. Only in two cases lack of funding resulted in decline participation in project (at the very early stage). I think that it is the question of clear research plan, some organizational skills and peoples' motivation. And it is applicable for rather simple research schema.
In Poland we have also special national grants for collaboration, where Polish part is funded by goverment, or internal grants, funded by universities to support research activity. I suppose that it is quite similar to French solution, described in Peter Stockinger post.