Can You Swim Faster in Water or Corn Syrup?

I don't think so. I think that at the extreme (say, the consistency of peanut butter), the amount of force you expend simply in inserting and extracting your arms (that is, not in the direction that propels you forward) becomes excessive.

Change the density and the swimmer's buoyancy will change. Change the viscosity and the optimal swimming algorithm will change. As you increase a liquid's viscosity, the swimmer loses its ability to coast on the inertia provided by previous effort. At a high enough viscosity (given a swimmer of constant size and strength), it's as if the swimmer has no inertia. The movement of the swimmer and fluid will be effectively a function of what forces the swimmer is putting on the fluid at that point in time, because any inertia will immediately get "stolen" by the fluid.

For example, scallops can swim in water, but with a high enough viscosity (or a microscopically sized scallop), their swimming style would get them nowhere. See http://en.wikipedia.org/wiki/Scallop_theorem . At high enough viscosities, the best way for a human to swim underwater would be to grow new skin on the scalp and reabsorb excess skin at the feet.

Viscous fluids are better at stealing the effort you've put in, so you're going to have a harder time swimming in them, unless you can find a good way to push yourself along without donating your velocity back to the fluid.

You'd like it to be the case that all you have to worry about is pressure and force, but that's not always true. A chemistry major in my dorm once made a non-newtonian fluid just with water and the appropriate concentration of corn starch. The viscosity is not a constant in such a fluid, but rather scales with the force applied. If you struck it hard with a pencil, the pencil would bounce off like the fluid was solid--but if you pushed slowly, it would act like a thick liquid. It was like... a liquid chinese finger trap.

Since your hands move faster than your head, I think that means you would swim faster in such a liquid, up to a point, although after a certain point swimming faster gets harder to. It hurts my head to think about it though.

thanks for the explanations

No, pressure is not pressure. There are two ways a fluid or gas can exert a force on another body: through normal pressure ("normal" here meaning the local normal perpendicular to the surface of the body at that point), and through shear forces, which are dependent (mainly) on the viscosity of the liquid, but also local fluid effects such as boundary layers etc can come into play.

Density doesn't necessarily correspond with viscosity. Water's viscosity varies greatly simply by temperature. Water at 90C has under 1/4 the viscosity of 10C water, but we're fully buoyant in it.

Right -- this was my initial reaction. You can generate more thrust in a higher viscosity fluid, which will "cancel out" the increased friction, but it also takes more energy to generate the increased thrust, so you'd tire out more quickly.