Ok this may be a little cheesy but understanding the three approaches to designing a website or any other functional screen based product is essential. I often meet people from many different areas of the design and web industry who are fantastic in one area but respect little about another area. It occurred to me that these areas can be split into three. Branding, Interface and Coding. This triangle of areas all come under that general term of design. I rarely meet people who can do all three of these convincingly, what you normally get is somebody who is very good at one area who maybe gives the odd nod to the other two. It is my view that even if you do not actually perform the other two tasks it is at least important to understand them and value them because these three things all work together to create a successful site.
This article has been written from my own perspective and from my personal experience within the industry - it is a little bit of fun but I do feel that baring personal bias it is always important to remember these three areas in whatever context a website is being developed in whether it is a flash site, an e-commerce site or a corporate site. This article was originaly written for Attitude Design and can be read fully here: Attitude Design Post. Anyway - let me explain these 3 in short:

THE GOOD - BRANDING
As a graphic designer with a background in print and branding I do of course have a bias towards the branding area. Branding is the hero. He is blond, tanned, and handsome. As he walks through the taverns swinging doors one can almost hear the sound of a man whistling a famous tune. His voice is soft but firm and he embodies all that feels good and secure – he is Clint Eastwood himself.

THE BAD - INTERFACE DESIGN
The bad or Angle eyes is dark and dangerous. He dabbles where he is not wanted and makes very controversial decisions. He knows his opponent inside out and is a careful calculator of priorities and probability. He represents the dark art of interface design.

THE UGLY - CODING
The Ugly is, well ugly. He is complicated, a mess to those who do not understand him. He smells of late nights and geeky amounts of black coffee. He is very clever but is not really on the same wave length as the rest of mankind.

CONCLUSION
So which are you? Good Bad or Ugly? Do you know enough about the other two to give you a rounded approach to creating the ultimate website which is successful in every area. As I say read full article if your interested. Comments most welcome...

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Simple.

graphic design + interface design = web design

client-side scripting and flash (animation and actionscript) is a must

You could learn some server-side tricks on the way. Practise and learn - and organize.

And use a brain. Use what you know first.

Not all sites will require bulletproof security. Of course security should always fall on the serverside. I can't really agree with the OP though, a "web designer" is a dying breed. Being able to lay something out in photoshop or illustrator, and then passing off the design to a "coder" is a bad way of doing things. It is only after you know what can and cannot be done, and with what upsides and downsides can you a design a truly good website, without sacrificing the original vision. This sems to be an ongoing discussion. There was another post a while back about somebody breaking down the different roles in web "design". One of the words that came up was Front End Developer. This is the person who should be handeling things client side. The design, colors, usability, accessability, Flash, Javascript, etc. should be handeled by this one person (or team of people). Like i said, if you don't know code, the rules and the exceptions, you should not be designing for the web.

imho

>Being able to lay something out in photoshop or illustrator, and then passing off the design to a "coder" is a bad way of doing things

This is my point - all three of the above things must be understood at least otherwise you will not get the balance right. You need design and functionality working together. If you can combine all the areas above into your skill set you are a winner...

If not at least get a team which can do the areas you are not so hot it. However every member of that team needs to at least understand and repect the other areas for you to be successful. Thanks for the comments.