Battery Calculations
Actually, the calculations for the battery requirements aren't that bad:
If you use 4 Trojan T-105 batteries (these are 6-volt golf cart batteries) you'd set them up as two strings of two batteries, giving a battery pack with 12 volts and half the current flows comes from each string. So, to use Ross's example where steady motoring at 3.6 knots requires a steady 63-amp current from the battery pack, each of the two strings will need to be supplying 32 amps. This would be a total of 250lbs of batteries.
Now, if you look at the specs for the T-105's you'll see that they have a 5-hour rate capacity of 185 amp-hours. That means that you can pull 37 amps out of them for 5 hours if you completely drain the battery from fully charged. Of course, you should never do that: You shouldn't take even a deep discharge battery below 50%, so that gives us a limit of about 2.5 hours. In other words, you should be able to use a pack of 4, T-105 batteries to provide a steady 1-hp of drive for 2.5 hours before you need to recharge.
This is quite a bit more than just getting in and out of your slip, but isn't going to get you down the ICW, or drive you into waves, against currents, etc unless you have a generator connected to provide the power when needed. If you're a larger cruising boat that was going to have a generator anyway, this hybrid approach might be a nice way to go. If you're a small sailboat and in/out of the marina is all you use your engine for, the batteries-only system might make sense. The mid-size vessels are where the economies of marine electric drives are still rather dubious.