This is a pretty difficult question to answer as there are so many different databases available. If you can provide more information about the particular discipline(s) you are interested in, it will be easier to point you in the right direction. For example, my research is mostly focused on insect systematics so I tend to use the Zoological Record (http://thomsonreuters.com/zoological-record/) and Taxonomic Literature II (http://www.sil.si.edu/digitalcollections/tl-2/index.cfm) most often. I also use BIOSIS (http://thomsonreuters.com/biosis-citation-index/), Scopus (http://www.scopus.com/home.url) and BioOne Abstracts & Indexes (http://search.proquest.com/bioone). Most university libraries maintain subscriptions to these databases.
For general biology (including medicine and all other topics in biology): Web of Science/Web of Knowledge (http://apps.webofknowledge.com) if you have a university access or Google Scholar, which is now getting much better than it used to be. PubMed is also very good but it focuses more on medicine.
I think Pubmed Central (http://www.ncbi.nlm.nih.gov/pmc/) is the best place to find recent quality articles that are open access. Another way round is to check Pubmed. you will only get abstract over here in pubmed (http://www.ncbi.nlm.nih.gov/pubmed/). Almost all good biology journals are indexed in medline and hence are available via pubmed. Hopefully it helps...