In order to sort out the mis-information, it's important to separate canvas as a material from people's memories of outdated tent designs. Many of the tents people recall with not-so-fond memories wouldn't have been any better had they been made of materials other than canvas.
Canvas as a tent material has some specific advantages and disadvantages:
Advantages:
"Breathability" - Cotton canvas is unmatched for breathability as a tent material, unless you count mesh screens. Most modern synthetic tents use lots of mesh under a rainfly to allow the tent to breathe and prevent it from getting clammy inside, however they don't do a good job of holding in heat. Canvas can be zipped up tight with no rain fly, and still breathe to a degree. When cotton canvas is dry, it passes a small amount air through its weave. More important to reducing clammyness, is the way it absorbs moisture from the air inside, and then evaporates it to the outside. Of course, ambient humidity and temperature play into that, but in general it allows for more comfortable conditions inside the tent, as compared to synthetics.
Water resistance - the mechanism by which cotton canvas resists water is by absorbing it. That is, the fibers the canvas is woven from soak up small amounts of water, which causes them to expand. When the fibers expand the weave tightens up, and resists water from passing through. When sewn with proper thread (a cotton-sheathed, poly-cored thread), the thread expands to tighten up its holes as well, so a "seam sealer" isn't required either.
Modern treated canvases have a treatment that limits the amount of water the fibers will soak up, yet still allows enough absorption to swell the fibers and tighten the weave. You see this as water beading up and running off the tent while it stands in the rain for hours, yet when the tent is dry, it is dry to the touch (no old-fashioned oil or wax treatments). Also, the old adage "don't touch the walls or the water will soak through" isn't quite true anymore. For some canvases (such as Sunforger--probably the best available these days), the treatment is applied to the threads before they are woven into canvas, making for a very robust treatment.
Quietness - canvas tents are so refreshingly quiet in the wind and rain. My Jumping Jack trailer uses a Springbar-style setup, which stretches the canvas so tight it's a bit like sleeping under a drum head (it does get quieter as the tent roof soaks up some water). However, spending a night in the rain in my friend's synthetic ground tent reminds me of just how loud the alternative is--especially when the wind picks up.
Disadvantages:
Drying after use - this was already mentioned, and is certainly the biggest hassle when using canvas tents. On the other hand, you do have to dry out any tent before packing it away after it's gotten wet, you just have to be more thorough about it with canvas.
Weight - this almost goes without saying. Everybody knows canvas is heavy, and there's not really anything that can be done about it. Some wall tent makers use synthetic materials for walls and other areas of their tents, to try to cut weight while keeping some of the advantages of cotton canvas.
Cost - good quality canvas is surprisingly expensive. If you think of it as an old-fashioned material, you'll be quite surprised at what items made from quality canvas go for these days. However, canvas is still very long-lasting, especially with modern UV-resistance treatments, which helps justify the price somewhat.
All in all, based on the my own experience with modern canvas tentage over the last few years, I will say canvas is the top choice in the rain, wind, storms, and cold temperatures. For me personally, I would select canvas as a tent material of choice for any use except for when I have to carry it to camp on my back.
I already mentioned my Jumping Jack trailer's canvas tent, but my cousin bought a
Kodiak Canvas cabin tent a couple years ago, and we've been camping with them as well. He bought the accessory awning with side panels for his tent. He sets up a table and rug inside, and even in heavy rain, you can close off the side panels and have a comfortable, dry place to hang out and cook, eat, read, relax, etc. inside.
That cabin tent is certainly an old-fashioned design, but it does have a poly "bathtub" style floor. Setup is quicker than I would've expected for just the tent, and don't forget that with canvas tents, there's no rain fly to mess around with. However, the awning accessory on my cousin's tent takes longer to set up than the tent itself does. Overall, his tent works well for what he wants it to do, and he doesn't seem to mind the pitch or strike times involved. If it were me, I'd have gone with a Springbar (or Kodiak's Flex-Bow) design instead.
I've also looked at the designs from places like David Ellis, Beckel Canvas, or Snowtrekker online, and there sure are some nice canvas tent designs available these days. One thing to keep in mind with ordering tents from places like this is the fact that you can have custom options included fairly easily--after all, you are commissioning a tent to be sewn just for you.