Addressing myself to some of the newer photographers or those contemplating buying their first dSLR, here's some things to think about.
Assuming that 90% of what you do is landscapes, then I raise the following points:
1) Anyone serious about landscapes uses a tripod - too many shots need f16 and a slow shutter speed to manage without one unless you are limiting yourself to dreamy narrow depth of field or even motion blurred images.
2) once on a tripod, the only reason to be concerned about shutter speed is a) wind and b) water. The former needs either patience or a moderately high shutter speed, the latter requires slower speeds to get nicely blurred flowing water.
3) very few landscapes need shallow depth of field so paying for wide f stop lenses is both a waste of money and extra weight to carry round - unless the lens is demonstrably better than the slower one - I replaced my f4 70 - 200 L lens with the 2.8 LIS because on a full frame camera the f4 just didn't have it at the edges never mind the corners. the new f4 IS is I understand just fine in this regard.
4) resolution wide open is rarely an issue and while it's true that stopped down variations in lens quality are less, sometimes they are still very siginificant, especially at the edges.
5) while many kinds of photography de-emphasize corners, landscapes typically have important information right into the corners and seeing fuzzy branches in the upper corners or blurred grass in the bottom ones is disturbing - so lens resolution in the corners is important, much more so than say in portraits or fashion or sports where centre sharpness is more important.
6) for most but not all photographers, extreme wide and extreme long lenses tend to be used less commonly in landscape work and all things being equal it makes more sense to pour your money into better glass than longer or wider glass. Once you determine a strong preference for wide or long images, you can get a second lens to cover the extremes.
7) these days zooms can sometimes be as good as single focal length lenses so avoiding zooms isn't necessarily needed and given the issues of framing and cropping, good zooms are perfectly reasonable for landscape work.
8) all things being equal, extreme range zooms (> 5X) are walk around snap shot lenses, not ideally suited to landscape work.
The perfect lens would be 10X zoom, F1, light weight, cheap and extremely sharp at all apertures, oh, and it would be nice if it had no barrel or pin cushion distortion.
There are no perfect lenses, not even close. Whatever lens you buy, even if you eliminate cost as a factor, is going to be a compromise in speed, size, range and so on.
Let's look at Canon equipment for a moment, simply because I know the most about it. Let's say that you are on a budget so you are buying a reduced sensor size camera, and probably not the top model even at that - so you decide to get a Canon XTI (400). Nice competent camera, good enough for the vast majority of even serious photographers. Remember, I'm limiting my look at Canon and am more concerned about lenses than camera features, so:
I'm an aspiring landscape photographer on a budget. I have just graduated from a consumer type point and shoot digital camera and for whatever reason I have purchased a Canon XTI.
The camera comes with a budget 18-55 lens that isn't IS, isn't fast, and isn't terribly sharp (I'm hearing there is a new model out but haven't seen reviews of it yet so can't comment on just how good it is). I could spend a bit more and get the 17-85 lens, no faster but it has IS and is decently sharp at the centre. Corners are fair but hardly wonderful, the lens is small enough for a walk around lens but that isn't all that important to me.
The 17-55 f2.8 IS is reputed to be very good, though larger and faster, the latter unneeded for the kind of work I do, and it would have been nice to go a bit longer on the long end.
I could get the 24-105 - good lens, a little soft at the long end but on a reduced frame camera, not even an issue. It is heavy though, rather like the camera sits on the the lens rather than the more typical other way round. Still, in one lens it has a decent range (remember the 1.6X multiplication factor) so it's better at the long end than the short. 24 mm. X 1.6 = 38.4, barely into wide angle territory. I can see getting frustrated at the wide end pretty fast. Still, Canon makes a reduced sensor lens, the 10-22 which is very good and not all that expensive, but now we're looking at $1000 for the 24-105 and then pay for the 10-22 - not ideal.
I could look at the fixed focal length lenses but by the time I get a decent range of them, and live with the limitations of fixed lenses and the hassles of multiple changes and sensor dust, I'm thinking that is not looking very attractive.
One option that could work for most landscapes is to forego the really wide and use stitching of multiple images when I need wider. With a bit of care, this is an entirely viable option, now that 24-105 is looking to be a better choice, the 17-85 a decent option if on a really tight budget.
Is it possible to really save money and shoot good landscapes - sure it is. You could limit yourself to a single lens - say the 50 mm 1.8 which is dirt cheap, fast, light, and very sharp when stopped down. It's a little longer than normal with the 1.6 X factor but you could stitch for wider - definitely an option for the financially challenged photographer who needs top quality.
Having said all of the above, a good photograph is infinitely more important than an image with sharp corners. The image you get is infinitely better than the one you don't.
In the end, were I tight on funds and starting out in landscape photography, I'd probably get the 17-85 and live with the limitations. If I were a bit more flush, I'd plan on a two lens system asap and go with the 24-105 (which would still be a good lens if and when I upgrade to a full sensor camera) along with the relatively inexpensive 10-22.
The 24-105 is a good walk around lens, if you have a Sherpa, but the 17-85 ain't bad and makes a very nice walk round lens and keep in mind that you might not always be a landscape photographer, if it's painless to explore other venues.
I remember seeing a full page magazine image of a beach shot with the 75-300 Canon lens, a remarkably mediocre lens, but the image was every bit as sharp as anyone could want, and besides, the guy had it published - what more does anyone really need. In the end you have to read reviews, including this one with a large grain of salt. It's where you point, not what you point that counts.