I pretty much completely furnished a two bedroom apartment here almost exclusively with basics from Ikea for about $3,500. Granted, we went with their bottom-of-the-line stuff, shopped sale items, and got the couch and living room chair on a "discontinued" sale. We initially had only what we carried over in two suitcases, and pretty much got a full set-up, down to the dish towels and spoons and including three large bookcases with glass doors (again, a discontinued color). I filled in with items from local charity shops (which are good places to find things like jackets and pots-and-pans).
[We sent the rest of our stuff over slow-boat, so save money, through Rainier and it cost about another $5,000 door to door from California, with full export packing. We had a LOT of books, but everything fit into two and a half standard sea crates. Rainier's slow-boat service bills on size of crate, not weight, so whatever fits goes. They did a great job on short notice.]
Things I regret not bringing: my American rocking chair (now replaced with a similar, but not quite the same, from the British Heart Foundation second-hand shop after a very lengthy search); electric stand mixer; wooden hangers (the ones I am finding here are not as large and so the shoulders of coats sort of hang down); food dehydrator; crock pot; stick blender; desk and short-wave radios (that plug in). I was able to buy a couple of step-down transformers here that take two extension cords each and will run up to 1100 watts (continuously) per unit and could have handled any of the the above, at about 60 pounds each. (They are completely silent and are designed to run continuously.) Replacements for kitchen appliances and other electronics are expensive here, we've found, and we are kicking ourselves for giving away the good-quality ones we had in the States. The Daughter wants a small radio that looks nice and also plays CDs and has a USB port, and runs on mains power. The cheapest I've found (that doesn't look like a boom-box) is almost 100 pounds. We brought the turntable (and my 500-lp record collection) and it's working fine on the transformer. Also brought the tropical fish aquarium stuff (heaters, pumps, etc.) and they're fine as well on the transformer.
I regret not bringing more linens. I did bring several American-style quilts (which you won't find here) but did not bring any sheet sets. I'm having a devil of a time finding top sheets - everything is fitted and they seem to assume you'll be using a duvet, for which they sell duvet covers. And it's hard to find 100% cotton sheets that are not expensive. Most sheets seem to be a blend with a synthetic, in the lower-end stores.
Jeans. Definitely. For all the reasons the others have stated - and because they're still wearing those jegging-style jeans here, and skin-tight-to-the-ankle jeans as well. Daughter's puffer jacket - we had a good one from Lands End, left it behind. The ones we see in the store here look like they're made out of bin liners. Really regret not bringing that puffer - it squashed down to nothing in the space bag but the kiddo said to donate it, so...
Should have brought bottles of familiar seasonings (Mrs Dash, good quality vanilla, Lawry's, etc.) and things for the medicine cabinet: you can't get things like Neosporin here without a prescription. Naproxin the same. Ace bandages - we had some sent over after dealing with the local variety, which are not anywhere near as good. The replacement for the water-pick would be an eye-watering price, so we're doing without. The electric toothbrushes were three or four times what we'd have paid in the States.
The dining room rug. I had a woven rug that I now wish I had brought. Got it at World Market or Pier One (not sure which) and there is nothing like it here at all. Plus, replacement rugs are not cheap here. We weren't sure if we'd have carpeting or bare floors, and ended up with bare floors, so I'm always on the hunt for rugs/room rugs. A desk lamp and our living room stand lamps. Again, replacements are terribly expensive here, and switching the wall plug (or using a plug adapter) and changing the lightbulb out (to a LED bulb, with a socket adapter) has worked well for the one lamp we did bring. Kicking self for not bringing the others.

We donated a massive amount of our stuff to AmVets before we left. I wish I'd known then what I know now, and I might have brought more than I actually did.