Essentials for
long trips in remote places.
Mmmm, depends...on how long is long, and where is remote.
If different climate zones are part of the tour, especially mountains, then your tent, sleeping bag and clothing have to take account of that.
I don't do winter touring/camping, so my gear is all of the two- or three-season variety. In recent years, I've cut back on weight and bulk in tent, bag and mattress by buying new stuff. It's pricey, but for the quality and weight/space saving, it's good value. (Examples: one-person Tarptent; Western Mountaineering 0/32F bag; and Thermarest Neo Ultra light mattress.)
One thing I use, not mentioned so far, is a lightweight (ripstop nylon/silicone) tarp, about 7' x9', weight 400 gms. I like to have extra shelter from wind and rain, so that I have a dry space outside my tent.
Does your "remote" mean no settlements/farms, etc.? My hiking or paddling in such country (Southern Africa and Canada) means carrying food for, say 4 - 14 days. This requires a lot of dehydration, and/or caching supplies beforehand.
I don't cycle in those conditions, but there are parts of Eastern Ontario, where I live, where I might not pass an open food store in a day's ride. In those situations, I usually carry food for a couple of days. Similarly, on a monthlong trip in the Rocky Mountains & Cascadia two years ago, food stores & places to eat were sometimes few and far between (though more common than in many parts of rural Ontario).
One key consideration is water. On my Rockies trip, I had water bottles with 2.5 ltrs capacity, and had a 2 ltr bladder as backup -- I used that a couple of times. I took along water purifying tablets as well, and used those a couple of times. (Check Dan's budget for carrying water, however, on his trips into the Great Basin of eastern Oregon -- that's a wholly different proposition.)
On my cycling trips in Eastern Canada, conversely, I don't take extra water capacity, as I'm rarely in areas where there are no people for any length of time. On paddling trips (in W Québec), I refill my bottles from the lakes, and carry a filter just in case.
Cookware: If you're doing any complex cooking, I'd recommend a stove such as the multifuel MSR Dragonfly, which has a good simmer capability. With that, however, you have to plan your carrying capacity (the stove is very light on fuel, tho'), as well as the availability of fuel. I use my MSR on paddling trips, where weight is less of a consideration than on my bike.
If your cooking is mostly boil-water-and-add-dried-stuff, then a Trangia alcohol stove is very light & compact, though it doesn't really simmer. I use the Trangia on my cycling tours, where I usually find a place to eat once a day, sometimes more often.
Hope that's helpful.
Cheers, John