I am going to list some of the databases I believe people should know about and probably have access to if they are at a university. + some other stuff.
Chemistry. Free stuff.
http://www.webelements.com/ Element information CAS-Registry numbers, NMR properties etc. I used it mainly for the NMR properties (left hand column)
http://www.sigmaaldrich.com/technical-service-home/product-catalog.html Lots of data and for common and not so common chemicals.
http://pubchem.ncbi.nlm.nih.gov/ Sort of a free (but not as good) Registry database.
Chemistry.
Someone has to pay a small fortune for these, but if you have access to a university computer or library
chances are they have. If you are masters student or going for a PhD, learn how to use these, they will increase your productivity by a significant amount compared to Google Scholar (which is still a great and free complement due to the ability to search in full text sometimes) and they are a great way to find out what research groups are doing interesting stuff. There is a reason your library is paying for these databases. The same applies to the commercial general ones.
https://scifinder.cas.org/ The best database for chemistry articles and patents (more new compounds are indexed from patents than from articles, no reason to limit yourself), great refinement options etc, reaction searching, structure searching, you name it. It is also the largest chemical compound database in the world. You probably have to create an account for this and most likely your university only has a very limited amount of simultaneous users. Uses controlled terminology
https://www.reaxys.com Contains Beilstein and I believe Gmelin. And have been supplemented with various patents and quick synthesis descriptions (these are great), great resource for chemical properties. Very good tools for making schemes of multi step reactions. Not so good for text searching as they do not use controlled terminology.
http://www.hbcpnetbase.com/ CRC handbook. You probably have one lying around in the lab.
General .
http://www.harzing.com/pop.htm interface for google scholar making certain searches a lot easier.
http://www.scirus.com Elseviers free database.
http://www.espacenet.com/index.en.htm A free and very good resource for patents. Do realize that most people want to hide their patents. If they get away with it, the document will be named: A new device. Learn to use IPC NCL and ECLA codes if you want to be really efficient. You can manage going through uni without being able to search patents but why not get that extra edge. There is also often the option of finding English language equivalents for patents in other languages.
General but commercial. If you have access to a university library or a university ip-adress chances are good you can access these. If you have access to these databases learn to use them instead of google scholar especially if you are in natural sciences or medicine. Getting 900 hits sorting them by numbers of citations, then picking only the review articles from the last 5 years in a language you can read is superior to wading through the hits in Google scholar.
http://apps.isiknowledge.com/ Web of science. If you have access to it use it instead of google scholar The sorting options and refinement options are so worth it, Chances are you can also access myendnoteweb, to upload all your references directly
http://www.scopus.com The commercial Elsevier competitor of web of science. Web of science is better for older stuff but Scopus contains a large portion of Compendex which is one of the best engineering databases out there and also more non English journals. Use the add categories option to be able to sort between keywords, document types etc.