no mod cons  

That's easy--
After electric light, I'd nominate the computer.

Well, picking just one is tough...
and I'm not a big gadget-head, although 'the hubs' is. I love my iPod best, I guess. But I must say that the GPS comes in a close second. It's very handy for driving around this big empty state of New Mexico.

Gadgets?
To me, "household gadgets" are things like kitchen tools or small appliances. My list, in no particular order, of those types of gadgets that make my day-to-day life easier: Rice cooker, Bamix, stand mixer, blender, Thermapen thermometer, silicone oven mitts, microplane, George Foreman grill, laser level, cordless drill, EdgePro Apex, Rabbit corkscrew, nonstick cookware.
If we're talking about a wider range of devices, then of course I agree with WHC about the electric light and the computer -- or, more specifically, the computer with high-speed internet access -- plus the other communication devices: phone, radio, television. And I wouldn't want to live without a refrigerator.

,
microwave

A good sharp knife...or in...
A good sharp knife...or in the alternative a good knife sharpener

Fewer and fewer for each year
My top five list of mechanical/electronic gadgets:
1. Wireless music transfer device
2. Portable music player
3. Rice cooker
4. Coffee grinder
5. Cordless screwdriver
These are pretty much the only gadgets I use regularly, and they also make my life more convenient. In the more general sense, I would put my wok and knives at the top of the list.

Fire
Fire!

Things
Most of the truly useful things are not 'modern' - scissors, matches, anglepoise lamps, wool lined slippers.
The few things that are truly difficult to live without in a modern sense are:
laptop
coffee maker
cell phone
comfy chair

Define gadget, I guess. The b...
Define gadget, I guess. The biggest gadget, of our lives at least, may be the TV, so completely ingrained in us, few people even consider groundbreaking this day and age the most grounbreaking feat we have come to know as the remote control.
Here is Composition, by John Ashbery.
http://writersalmanac.publicradio.org/index.php?date=2005/07/28

I would have to second the...
I would have to second the GPS. AS a life-long ADD inflicted mind, paying attention to directions is nearly impossible. Now I don't have to.

GPS
hmm.
Don't try one of those in New Jersey. : )
Not specific enough topic.
But recent problems solved...
If still in the work force. Far from retirement.
Coffee grinder Bunn LPG
coffee pot Chemex
travel mug JoeMo
And a new SwingAway can opener.
I'll never need it but i'm always afraid a good
classic product that never breaks will put the
company out of business. (oxo sucks)

3 things I cannot live without
1. Cheap but delicious Cote du Rhone wine
2. My Nespresso machine
3. My Westin Heavenly Bed mattress
Well, I suppose, in a literal sense, I could live without them but then that goes into the whole quality of life question, doesn't it?