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I just noticed today that my 4.5 inch RES has water drops underneath his eyes when he is basking. It almost looks like tears that just kinda hang right underneath his eyes. Of course, once back in the water the tears go away. When he first got out to bask there were very small droplets and I thought he might just still be wet, but when I waited for him to dry off while basking the water stayed under his eyes in droplet form until they eventually ran off. It is not slimy at all, nor did the "tears" appear everytime he was basking today. All other behavoirs and health of my turtle are normal. I plan on doing a complete water change tomorrow to see if anything changes. I read that in marine turtles there are salt glands located near their eyes that constantly filter excess salt. Is this normal for RES as well? Has anyone else noticed this in their turtles?

Sounds normal - though watery eyes with other symptoms (runny nose, listing) can be a respiratory infection. I haven't researched this topic (the lachrymal gland) but I have observed something similar with my RES as well. Areas with sensitive tissue like the cloaca tend to be cooler and more moist.

Someone once told me that their turtles "cried" sometimes, and I wasn't sure what they meant. However, I have noticed that my RES will appeared to get teary-eyed, both when basking for a long period of time, and when he's been walking out of the tank, particularly outside. I think it's lubrication to keep the eyes from drying out. In the absence of any other symptoms, I wouldn't be concerned about it.