I have no experience with riding mowers, but I have been using a corded electric mower for years. I love it - nothing but the smell of fresh cut grass! The cord is not a hassle at all once your used to it - provided that you have few obstructions (e.g. trees, gardens, etc). It doesn't sound like that's what you are looking for though. Good luck with your search, I'm sure you will find an electric mower far more pleasant than a gas one.
As for electric outboards, I have a Torqeedo that I have used to push my sailboat in and out of the marina. I have had it since summer 2011, and have had zero problems with it. I wrote an extensive review including some cases in which I would not recommend it here: http://forums.sbo.sailboatowners.com/showthread.php?t=131151
. If you have specific questions, I'd be glad to answer them. It really is the only electric outboard in the market (that I can find). There are plenty of low-speed trolling motors, but this thing can really haul by comparison (it's equivalent to a 4HP gasser). It also weighs less than a trolling motor + lead battery.
Edit: I guess I shouldn't say "zero" problems with the Torqeedo. It has occasionally thrown an error, but a simply reboot has always cleared it. This typically happens when I am fishing - I will use the motor for a minute to position the boat, and then stop it for half an hour and drift. Rinse repeat. The motor hasn't given me troubles while it was running.