In my experience, the best place to start is almost always Pub Med. Pub Med is incredibly comprehensive; as of October 2011 it has indexed more than 21 million records going back to 1809, with another half-million articles added every year.
I’ve accumulated a lot of these strategies over years of trying to track down papers for FDA regulation purposes.
Some might be obvious (especially to grad students or other researchers), but I still think it worthwhile to mention them.
Sadly, is reasonable compared to some journals.
I’ve seen journals that charge more than USD per research paper – even for ones 20 years old! There are a number of ways to legally access scientific and medical research without paying ridiculous per-paper access fees.