If you're looking for data from already published works I usually read the literature -- most journals require data to be submitted to data repositories. I then comb SRA, ENA, and DDBJ for public data for meta-analysis that was cited in a study I am interested in.
Not sure about non-American databases, but typically what I do is go here "http://www.ncbi.nlm.nih.gov/" and in the Search Field I pick "All Databases" and then enter the species I am interested in. For example, if you enter "glomus", you will find "http://www.ncbi.nlm.nih.gov/gquery/?term=glomus" that there are 17 SRA experiments (NGS data), but also there are many submitted Nucleotide sequences as well as predicted ESTs. It's a nice page because it gives you a nice overview on the type and amount of data available.