I also have an EU2000i. Haven't had to use it in an outage yet, but I know it'll work. After sitting - totally unprepared - for several days without power last winter, I started looking for options. While a whole-house generator was really tempting, the vast majority of residential-grade stuff that was reasonably affordable uses air-cooled engines that are extremely noisy, VERY thirsty, and apparently don't live very long when you look at the rated lifetime hours info. I also wasn't too keen on eating up a chunk of the backyard for something I may not need but once in a blue moon. A portable would also be useful to others - just as I got my power back last winter, my parents lost theirs.
When I started sizing generators, I was a bit dismayed by the charts I found online. If I believed them, I needed something in the 4-6kW range minimum. But I started logging peak power usage for the devices I wanted to run (furnace and fridge, mainly) and found their peak and average draws were considerably lower than the online guides listed. While the EU2000i is not going to have much spare for other things while running the furnace and fridge, I decided to go with it because it is still easily carried around and those things don't run continuously anyway - I can let the furnace cycle off, then do other things.
To feed the power in, I opted to install a dedicated generator circuit. I put in a locking power receptacle in the eave of the house near where the generator sits out back, and fed three outlets, one in the back of the house, one in the kitchen, one in the garage by the furnace. I then just set up the generator, get it running, and plug in the things I want to power off of it. No cords through the doors or windows, no worry about backfeeding or messing with the breaker panel.
I test-run the generator each month, actually hooking things up. Usually I'll plug the furnace in, as even with A/C running it'll still run the blower, sometimes the fridge or the computer. Let it run an hour. Been doing that since around May, and I still haven't used the first gallon of gas I put in it! The EcoThrottle feature definitely conserves fuel. In contrast, some of the cheapo generators my friends bought will go through a gallon of gas in less than an hour of operation with no load. I bought a 5-gallon gas can, put StaBil in it, and thus have potentially a week's fuel supply for the Honda - as opposed to tank-farm sized requirements to run some of the other generators I looked at.
The low fuel requirements do pose an issue - how to keep the fuel fresh. But between the StaBil which many have assured me works wonders, and the fact my cars use gasoline as well I'm not concerned. If I don't have an outage anytime soon, I can just dump the old gas into my car then refill the can with fresh. And if I have an overly long outage I can use the fuel in my vehicles to power the generator.
The Honda uses an inverter to produce AC power too, which besides the efficiency means it's clean power. Even my furnace has an (expensive!) electronic circuit board on it, so I wanted something that wouldn't put the electronics at risk.