The Web is Not Paper.
The web is a relatively new medium – in fact, it's often referred to as just that, 'new media' – and practical graphic design on the web is still less than ten years old, by all accounts. This fact means that plenty of so-called web designers are really just print graphic designers trying to transfer their old ways onto a compuuter screen. What you have to remember though, is that the web is not paper.
Paper Doesn't Scroll.
If you design a site as if it had to fit entirely onto one sheet of A4, you're doing your visitors a disservice. Text on the web has a potential infinite amount of space. Why make me press a button to go to your next page? Are you stupid? Are you just trying to increase your pageviews and ad views, or what? Stick to the rule of one page for one article, and you'll do much better.
Paper Has No Bandwidth Issues.
You can cover a sheet of paper in all the pretty pictures and backgrounds you like, and it still doesn't take any longer to pick it up and read it. That's just not true on the web. I'm sure you abandoned dial-up years ago, no doubt, but there are still plenty of people out there using the web at those kinds of speeds. It's downright rude to make them sit and wait while your design loads, when all they wanted to do was read some text.
Columns Work on Paper.
One of the biggest issues with print designers find it difficult to get over is the web's lack of columns. You really, really can't do columns on the web. You just can't. It doesn't work. You have to spend hours writing a set of custom scripts, only to break functions like text selection and browser resizing that your visitors would rather have seen work properly – not to mention that reading left-to-right on a computer screen is unexpected and altogether quite unpleasant. Get over yourself, and leave your columns on the paper, where they belong.
Paper Isn't Linked.
One of the easiest ways to spot a site designed by a print guy is by looking for the links. If there aren't any, the chances are the designer used to do paper layouts. Even more so if they've added notes like 'go to our downloads page to see...' – you can link to it, you know! Don't be afraid to link far more than you'd think is sensible. Linking is what the web is all about.
Paper Will Only Be Seen One Way.
Web pages, on the other hand, will be seen in a variety of web browsers, at all sorts of sizes, in lots of different fonts... the list goes on. It's daft to think that you can control the way your website looks to every visitor: what you're doing is offering a set of guidelines, for their software to interpret however it wants. If they choose to make all their fonts massive because they have trouble seeing, who are you to set your page to override that? Yet many designers do.
Never forget that your role isn't to make sure that everyone sees the design exactly as you intended – what you're trying to do, really, is let as many people as possible see the site, and make it look as close to the intended design as possible, if it doesn't interfere with their wishes. That's the difference between a user-hostile website and a user-friendly one. If you're not a print designer, you're probably nodding your head – and if you are then, well, I suggest you take some time to think it over.
The End of Paper?
Paper and the web aren't adversaries by any means: the web is highly unlikely to destroy paper layouts as we know them, no matter how many 'technologists' might predict it. The important thing, though, is that paper and the web are different, and you need to realise that their differences are something to be celebrated, not worked around. The best layout for the same content will be very different on the web to the way it is on paper – but, in the end, why is that bad?