If that isn't a demonstrative example, what specific devices _would_ be useful to have Internet connectivity, and in what specific ways?
Irrigation system: I shouldn't need to punch buttons on a controller box outside in the rain.
Anything with a clock, e.g. microwave, thermostat: It should get the right time itself.
Pool heater: I should be able to control it from the house and check the temperature.
Barbecue: It should let me know if it was left on (like happened yesterday).
Freezer: It should let me know if the door is ajar, before everything thaws.
Alarm system: monitoring and control.
Stereo: should be able to control from my phone.
Washing machine: notification if I left wet clothes in it, or if it goes off balance and stops.
These are mostly available now, but not in an easy-to-use way. Home automation seems to be like the home computer industry in the 1970s: you have to really want to do it, you need to be a bit of a hacker, it costs a fair bit, and what you end up with is pretty primitive. I think there's a huge market for someone to solve home automation. What I want is when I buy an irrigation controller from Home Depot (for example), it "just works" as part of a home system.
Edit: A couple people asked why connect to the internet? I should be able to do these things remotely, e.g. from the office or my phone.
a_c_s mentions that the time tinkering could outweigh the benefit. That's kind of what I'm getting at with my 1970s home computer analogy - you could do e.g. word processing back then, but it wasn't worth the difficulty for most people. Now non-technical people can buy a computer at Best Buy and easily do word processing. Likewise, home automation needs to become something that is built in to products and "just works" by default, rather than something for hackers.
That is my #1 use case for me - I would love to have some view of our home to tell me that I haven't left anything on when we go away for a few days.
Though to be fair there wasn't any visual notification of its state - the light is only on when it's preheating.
The interesting thing is that I never need to look at the pictures - the mere fact they exist is enough to keep my happy....
[My family do indeed think I am crazy]
I can see them being WiFi-enabled and able to talk to each other and some type of centralized control system in the home, but why would that need to connect to the Internet?
However, for me, the amount of time 'saved' for tasks like this seems like it could easily be outweighed by having to spend even a minimal amount of time tinkering/debugging the setup of these devices.
Given that my phone sometimes forgets which wifi network to use, I can only imagine having to reconfigure my microwave, washing machine, stove/oven, dishwasher, stereo, etc. occasionally. If each device forgets the wifi network infrequently, like once every six months, that means 12 times a year I have to configure wifi one of my six smart devices. This amount of reconfiguration is more time/frustration/effort than would be saved by the kinds of notifications listed.
It's interesting that you chose 6 months, because that's how often you have to change the time. :D
Read/write the on/off mode, and get text notifications with severity (Info/Warning/Emergency). This is not some nightmarishly complicated interface. I'm sure we can all visualize what a good cellphone app would look like.
It seems like the big hurdle with home automation is the lack of a standard server for all the client devices to connect to. The challenge will be getting these disparate appliance companies to sit down and agree to anything... that won't happen until a big player gets enough of them onboard to make it a "must-have" feature.
Remote status information on my oven and smoke-detectors and furnace and water-heater and water-detectors, while expensive, would also be fantastic peace-of-mind for the worrywarts among us - at any moment you know if your house is flooded or burning or whatever.
At a low enough price point, being able to turn off lights and stuff like that is great, especially if there isn't much setting up involved.
Lots of other things benefit from some sort of connectivity, being able to do data collection and monitoring over a network enables a much more passive approach (which I expect means more people will take advantage of the opportunity...).
An alternative that I haven't seen mentioned, but is supported, for some appliances: Your electrical or water supply utility could tell your dishwasher to delay its cycle in order for the utility overall to better balance its load.