Most folks I know who have emergency generators run them once a month
or so.

I just got one [lost power for a week last week] and note that the
manual says once a *week*. [Briggs and Stratton 5500 watt Storm
Responder]

That seems like a CYA suggestion. I run Stabil in my gas and will
probably go for once a month under load. What is a good load? An
electric space heater that draws a constant 1500watts or so? Power
tools that draw a surge?

I'm also going to build a little shed/doghouse for this thing. Has
anyone seem some good ideas for a 4x5 structure that blends into the
landscape? [I've been thinking of a scaled down chalet- a gingerbread
house- or a fake boulder as possibilities.]

Thanks
Jim

IME, most of them say weekly and certainly it wouldn't hurt anything. I
try to make mine at least monthly, shoot for every two weeks, more
often if I think of it and am around the genset. I originally only ran
it monthly though, for the first few years. They always say to let
them warm up to operating temp too, which makes sense to me. Besides,
mine is electric start and it keeps the battery topped off with a 15-20
minute run.
I do believe weekly is best though: when the fuel bowl deveoped a
pin-hole leak, I found a lot of sticky, gooey gunk in the bottom of the
bowl and on the float. Couple years later the fuel pump (pulse type)
quit, and when I broke it open, it had a good buildup of the same gunk
inside it. So, more often than once a month is probably good advice if
you want max longevity out of your machine.

I usually just go flip the Transfer Switch and let it power the house
as if there was an outage but occasionally will use two electric
heaters, just to let it run in a reasonably balanced/known load
scenario.
Also instead of the little batteries most of them come with (lawn
tractor batteries, really), I started just recycling my used/weakening
car batteries on it. I first did it because it was all I had around and
I wanted to genset to work, but it worked so well I left it on. Got 8
years out of the last one! If someting happens and you have to start it
a few times in quick succession or it gets hard to start as when you
overestimate the amount of Stabil it needs g, you don't get a low or
dead battery nearly so fast. In fact, I've never run it down with the
genset; they'll last almost forever compared to the smaller tractor
battery in my experience.
A can of starter fluid is also nice to have handy as long as it's
stored safely.
Oh, and watch the age of Stabil, starter fluid, things like that too.
It seems if you go beyond around 5 years they aren't likely to have much
"punch" left in them.

HTH

Twayne