The key is to think about a website's "design" as being four things, and asking yourself if they really all need to be updated.
For most companies, the idea of "redesigning" their website means waiting for it to look very out of date, then going to a website designer and saying: "can you make us a new one please, these are our company house styles, here's the content from our current site which you can re-use, and here's some extra material". If you're thinking that's not a great approach, well done; but I can assure you that's what most companies do. And not only is that more of an upheaval than a website may need, it's also correspondingly expensive.
The key is to think about a website's "design" as being four things, and asking yourself if they really all need to be updated. They are: the content management system; the structure of the site (the paths set up for visitors); the content; and the graphical design.
If you have a site of more than a handful of pages, and/or find publishing a new page harder work than pressing a button, you may need a proper content management system. Transferring everything over can be a major task, but it can be done while keeping exactly the same structure, content and look, so that no visitor (or company CEO) need ever know; things only change behind the scenes. This is the best example of isolating just one aspect of a website's design for updating. The modest but talented website designer we use here at BMON has done this for one of our clients quite recently, and the results were terrific. The company can now add pages in moments, run a blog and easily update content, without ever having to refer to someone who knows about HTML and web servers.
Similarly, you might be amazed how a website's graphical design can be completely overhauled without touching any of the content. If you're already using a proper content management system (such as WordPress, Drupal or Joomla), it's particularly straightforward. But even if your site is just a bunch of pages put up individually with Dreamweaver, it still might be possible to make major, sitewide changes to the look and feel at a fraction of the cost of a traditional website redesign. Again, our designer has done this recently (and there are several of our clients whose websites I'd love to let him loose on in a similar manner).
What about updating the structure of the site? Funnily enough, this needn't be as hard as you might think. In many cases, the content is all there, and is great, but it's just not linked and signposted in a way which helps customers. It might just need more obvious "next step" links at the end of every page, and better ways of letting visitors find associated products. A good brainstorming session should be able to work out if that's the case.
Finally, there's the content of the site. This is the one which probably requires the most investment to get right. It also happens to be the one which is most neglected in a traditional website redesign, mainly because most website designers don't understand what on earth it is you sell, so they're not going to be touching a word of your copy. If you're the kind of company which believes it benefits from getting outside help to write press releases and other articles, then you absolutely should be getting good technical copywriters to provide the content for your website. And if you have 250 pages of the stuff, then understandably that's going to require a serious budget. If you do all your own writing, it may seem like a daunting task to update and improve all the content, but there's no reason why it can't be a gradual task, starting with the most visited pages.
How many of the aspects of a website's design need updating on your site? If it's only one or two, the cost could be far less than an unnecessarily major traditional redesign.