Some journals and conferences charge money before/after paper acceptance, similarly there are some which don't (like Open Access Journals). Does money matter in judging such journals/conferences before sending paper ? Unfortunately my organization is on a cost cutting and isn't funding for any such activities. Is there a list of journals which do not charge fees or charge modest fees, so that I can publish there on my own ?
I must disagree with the CS folks in the comments†. Whether a journal charges or not is immaterial to the quality of the journal. You can only gauge its quality by being an active researcher in that field, not by silly metrics (this is an order of magnitude worse than impact factor).
Different journals from the same publishing house might also charge different rates for publications. For instance, AIP publishes both the Phys. Rev. series (+ PRL) and the J. Acoustical Society of America. While there are no charges for the former set, JASA has "voluntary" charges for publishing.
Such "voluntary" charges are very common (some flagship and top-of-the-line IEEE journals come to mind) and serves primarily as an opt-out for researchers from low income countries in Asia/Africa/S. America. Researchers in N. America, Europe and Australia/NZ are expected to pay the publishing charges, since with the way grants are structured in these countries, there is almost always a specific budget earmarked for publishing costs. Of course, if a researcher has no budget or is publishing in his spare time or as a secondary interest, then they're also welcome to not pay the charges, but I've never seen anyone that's on a grant decline to pay charges.
† Opinions on this site seem to be overrun by CS folks, who generally state them as facts of life. From my years of experience in a variety of fields, I've found their customs to be more of an outlier than the norm (perhaps only mathematics has something in common).
Generally speaking, whether a journal charges money for publication or not should not be a criterium for judging the quality of one journal compared to another one. Use other means for that, for example checking where good papers are published, the academic reputation of the editorial board, opinions of colleagues, and, yes, even numeric factors such as the impact factor of the journal.
There are very high-quality open access journals, for example the PLoS series of life science journals, but also no-quality open access journals, for example the ones produced by most of the publishers on Beall's list. Some very high-quality non-open access journals ask for page fees (or even submission fees, as I learnt recently), others don't.
I am not sure whether there is a specific list of journals which don't require paying fees, or an overview listing publication fees for a range of journals. There is the quite well-known SHERPA/Romeo list, which distinguishes between different levels of self-archiving. I guess most of the green journals (highest self-archiving rating) listed there will be open-access journals and ask for publishing fees, so you could go and check the other journals in more detail, by looking at their instructions for authors.