Starting with (for me) what's makes fantasy really fantasy, magic doesn't exist (at least in the scope of our science and our collective understanding). Therefore, stories containing magic are fantasy. Turning to Sci-Fi, the big item is space flight. And while our current understanding of relativity precludes FTL travel, there is no reason to assume that we COULD NOT develop that technology. Therefore, FTL is a scf-fi artifice.
Using these rules of thumb to explore some common films and books, we determine that Star Trek, Babylon 5, and Battlestar Galactica are all Sci-FI (well, duh). We get to Star Wars, however, and things begin to get a little crazy. We have the ships, the droids, etc. that all point to Sci-Fi. But we get to The Force and we have to think awhile. If The Force is magic, then Star Wars would be a fantasy work. But very few (if any) people would NOT consider Star Wars Sci-Fi. Therefore, we have to find a way to explain The Force using the laws of our universe; it's not easy. Looking at the Lord of the Rings, the magic of Gandalf, Sauron, and Saruman clearly make the trilogy as fantasy. The same is true of the Wheel of Time series.
The biggest division seems to be magic - because our universe does not seem to include magic (certainly nothing in our scientific knowledge points to magic) it's presence essentially instantly indicates Fantasy.
The real stickler (and the item that led to this thread) is psionics. These abilities seem to be magical (or at least mirror magical effects) and yet they exist is what appear to be Sci-Fi realms. I believe we classify these abilities as mental (either as the product of different synaptic pathways, the usage of a higher percentage of brain capacity, or as some type of mutation). Of course, this leads to the introduction of a "Sci-Fi" element into a "Fantasy" setting and some people disdain that notion (or visa-versa).