I've never used a trailer; they're intriguing, though.
As it is, I've got a touring bike and panniers, and no cheap ones at that. So, I'm invested. I'm going with this setup until it wears out. Then I'll consider a trailer.
When I last bought a lot of stuff-- over the last 18 months-- I didn't consider a trailer.
When it comes to touring, it seemed to me that a trailer would be a sensible option. It weighs comparably to a set of four good panniers and two racks. (I calculated things along the lines of Mgagonlv, as I was getting Arkel panniers with aluminum frames.) It would likely result in less wind resistance, too. My front Arkel panniers can get a bit boxy when they're full.
But I wanted to use my touring bike and bags for utility functions, too. There panniers have the advantage hands down. It's easier to carry just a bike with panniers on it down the stairs than it is to make two trips for the bike and trailer. Everything can be stored together, ready to go. You can bring a bike inside of a store, if need be, but you cannot do that with a bike and a trailer. Storing a bike and panniers in your office is an easier matter, too, than messing with a trailer.
And panniers offer levels of carrying capacity. You can attach bags when you need them. The trailer's either on or it's not.
This last fact, actually, provides panniers with one advantage when it comes to camping. Someone above said he'd prefer a trailer, because he could unhook it and head into town. But you can unhook panniers too. More importantly, you can leave one or two on; that way when you get whatever it is you were heading into town for you can carry it easily.
Of course you might add a front rack to a bike you use with a trailer. But if you're going to spend the money on one rack anyway, then the rear rack and additional panniers start to look like a good deal compared to the trailer.
A trailer can carry some heavy items, true. But I've carried a lot of stuff on my racks and panniers-- at least seventy-five pounds of groceries, and for about ten miles, too. I don't find myself wishing for more carrying capacity very often.
A trailer might be harder to see, too, at night, when a motorist expecting a bike to be about as short as it is without a trailer wouldn't realize you've got a significant extension behind you.