Is it normal for the over flow pan under my hot water heater to constantly have water in it?

this is not normal and should be taken care asap

I had this problem too. What happened was, when I replaced the water heater, the T&P valve would open up occasionally and let a little out. It turns out that when it's heating, the water heater will jack the static pressure of the water in my house's plumbing up pretty high, high enough to crack the T&P valve a little. Shut everything down, drain the water heater some so the pipes above it are dry, and plumb in an expansion tank. That gives the water someplace to expand into. That should fix your problem permanently.

several different problems could be causing this. high water pressure will cause temperature and pressure relief valve to open. normally the t&p valve is attached to a water line and carried to outside or a floor drain. if t&p line goes higher that heater, then t&p valve may leak into pan. 2nd possible problem; thermal expansion! if you have a whistler pot that you boil water in>it whistles due to thermal expansion, hot water expands increasing water pressure. I have put pressure gauge on heater and saw it go from 60 psi(pounds per sq. inch) to 120 in just a few minutes, which will cause t&p valve to open, especially if valve is weakened by high pressure (sometimes by just being new. 3rd reason; water heater developed a leak . My state makes plumbers give 1 yr full warrenty on heater replacement. You should call the plumber that installed it and have them check it out.

Michael; Its probably discharge from your pressure valve. Reduce your water temperature to 125 F, and it will stop.

either you have leaking around a heating element (pull off inspection covers to check) or your T&P valve is seeping, or you have a leak at the main water line connections you need to have a plumber look at it if you are not comfortable in looking at it yourself