I graduated last year and but I was working for a small web design company for 2 years before I started (in 2006). I’d agree with everyone about personal projects, but I wouldn’t recommend the idea of “I’d recommend that graduates seek out a variety of different professional experiences, working in companies both small and large”, sure that’s an option, but I don’t think going through multiple jobs is going to get you anywhere as it takes a while to really get into the flow of a workplace.

The most important thing you can do is work on things that are interesting to you, if you’re not interested in something, why do it? You’ll just make yourself stressed, unhappy and unfulfilled. These don’t need to be for paying clients either. The key things are: document why you did them, document how you did them, and what was interesting/difficult during the project. Even if the mini-project failed. This will demonstrate your passion.

I truly believe the most important thing a web designer/developer can have is passion, because if they are excited by something, they can learn it. If someone came to me and said “I know HTML/CSS, take a look at my designs, but I am only starting JavaScript, I’m really enjoying it though”, when my job spec said “Requires advanced JavaScript knowledge”, I’d hire them anyway – because they are keen.

I don’t think anyone gets anywhere if they see web design/development as a 9-5 job and means-to-ends to earn money.

The awesome people are the ones that want to learn what CSS3 can do to help make their designs better, the ones that are desperate for all browsers to support HTML5, the ones that stay up until the early hours trying to make their website load in half the time it currently does, the ones that aren’t happy with anything just being ‘okay’.