The hot water pot is a necessity, and you'll find one in the kitchen of most (although not all) Orthodox homes. This is how we can get hot tea and coffee on the Sabbath, and it's also useful if the cholent is too thick or you need hot water for a really greasy pot or to warm up a baby's bottle. It's not permitted to boil water on the Sabbath, but you can keep already hot water hot. Until the invention of the electric coffee urn, one kept a large pot of water on a covered stove top or some other form of covered fire. Even today, there are people who use this means. There are huge pots with completely flat covers and spigots on the bottom for this purpose - you can warm dry foods like bread or kugels on the flat top, so they're very useful. They also hold more water.
But. They require an open flame all Shabbat (covered by a sheet of metal) and are only useful on the Sabbath or holidays, since you really don't want them during the week. jonbaker doesn't like the idea of a burner going all Shabbat - what if it went out while we were asleep, filling the house with gas? I concur.
So. We use an electric hot water urn. And we use it all week long because it turns out that these urns produce water the precise temperature for perfect manual drip coffee. We make our coffee using "stove top" Melitta cones - we have a small one for single cups and a large one with a carafe for more - and have for years. Maybe freshly boiled water would be better, but I can make a cup of fresh coffee in just about the same time as I could make a cup of instant.
For Shabbat, we make a pot of extra strong coffee and put it in a metal thermos. This is a variant of the traditional "tea essence", which is extremely strong tea, and has the same purpose - it's already cooked, so adding hot water doesn't cook it any more. There are those who only use tea essence for Shabbat, but we're of the more common school who use a "kli sheini" - a second cup. We put the hot water from the urn into one cup and then transfer that to the serving cup, and then add the tea bag. This officially cools it to the point that the tea doesn't cook.
The thermos keeps the coffee warmish, so that we only need a relatively small amount of hot water to warm and dilute it. Again, it's better than instant, even by the following afternoon.
The current thing is to have a sort of electric thermos with a pump instead of using a party sized perkolator. Our last one had two methods of water delivery - a manual pump and an electric one activated by a button.
After two-three years, the electric pump was working poorly, but the manual pump wasn't working at all. We were having to use the electric pump on Shabbat, which is really bad.
The new one makes somewhat hotter water and is purely manual. So, we won't even have the occasional "oops."
On the other hand, the rice cooker is a luxury. I mean, I'm perfectly capable of making a nice pot of rice on the stove top. However, the short time I had one last December completely sold me on the appliance. It frees up a burner and a pot *and* it's one less thing to worry about. I just have to pour in the rice and the water and forget about it.