For everyday cooking, we have a cast iron pot that ends up being used for almost every meal. It was $50 from Farmers - go the no-name brand (while I would love Le Creuset I am just not committed enough to pay hundreds of dollars for one pot) - and serves us well. Only problem; it's not big enough! I often wish for a larger version, for when we're making chilli or other meals we make go a long way. And sadly apparently budget cast iron cookware is hard to find in gargantuan proportions.
As well as a few regular saucepans, which are mostly used for rice and pasta (or when we're too lazy to clean the still-dirty cast iron from the previous day!), we have a non-stick frypan, which is perfect for healthy stir fry meals, browning off anything, and pancakes and omelettes. At this point we just buy cheapies and replace them every year or so, but I am tempted by the spiel of things like stoneware as a long-term solution - have you tried stoneware, or something else that doesn't lose its non-stickness? Does it live up to the hype?
Baking wise, I have a largish stack of bowls (fortuitously, since they're mismatched, they all nest neatly) - mostly glass, in varying sizes, but one stainless steel one (good for whipping up egg whites - they do get fluffier faster in stainless steel) and a Tupperware one. It was pretty pricey (about $70, if I remember correctly) but its big draw is that it has splashguard lid - basically a lid with a hole in the middle - which is fantastic if you're trying to beat anything prone to splashing, like, say, cake batter - I clean specks of butter off the wall far less often now I have it. ;-)
I also love my handheld electric beater - while stand mixers are fantastic, in a small apartment I reckon this is better solution - and unless you keep your stand mixer on the bench all the time it's much easier for most things anyway - and gives me better control over my batter. I have thrashed mine - it's a bit over a year old but I'd say I've probably aged it about 10 years in that time. ;-)
In the appliance category I also have a Braun stick blender, which I use most often with its mini food processor - impressively grunty for a wee thing, it grinds nuts, pulverises chickpeas for felafel, and even managed to blend a cinnamon stick into powder for me once, when I was desperate!
For measuring I can't go past my scales - they are used several times a week and I'd be perfectly happy if all recipe quantities were in grams, as I often plonk the bowl on top and just tare the scales off between additions (actually, I often just do the addition in my head but that has resulted in near disaster more than once - living on the edge?). For when I need teaspoon measures I have a few options - for teaspoons and tablespoons I like my regular measuring spoons, but the big red spoon (actually measures 100ml) is pretty good for dolloping batter into cupcake papers. The shot glass measure is ideal if I need, say, a couple of tablespoons of oil or some other liquid - much easier to handle than a spoon.
For cleaning the bowl I quite like my Tupperware spatula - again, pricey compared with most - $30 - but it is firmer and gets all the batter out of the bowl (much to Mr Cake's dismay!). It also seems to be standing the test of time better than the Briscoes silicone equivalent, though sadly being silicone doesn't get the lifetime guarantee of other Tupperware stuff.
Last, but definitely not least, and probably the only unusual thing on the list - my kitchen computer! Made from my old laptop, pulled apart and reassembled in a neat wooden slot purpose-made by my dad, it's my main recipe source these days. I do use recipe books too - but more often bake straight from online sources, either other blogs or recipes I've already written up.
What couldn't you live without in your kitchen - and do you have lots of toys and gadgets, or do you prefer to keep it simple?