Very, very important. I can assure you that 95% of websites out there look terrible and don't attract customers at all.
This is my idea of 95% of websites http://www.lushlawnservice.com/
Here's a nice, sexy retro one. It also just happens to be the best web programming/design software out there: http://panic.com/coda/
Basically, the keys to good web design in my perspective (I'm 15, I know style) are nice smooth gradients (colors morphing to other colors...usually unnoticable though. Notice in the good link, there's a gradient in the word coda. there's a gradient near the border of the light-blue heading.
Another important aspect is proper padding and margins---look in the first crappy link and see that there's no real spacing in between content and background. Looks kinda shitty.
One more aspect is to use a nice, well-rounded font with a BIG size for the headings/titles and medium size for content/information. Also use borders, usually thick with gradients, to seperate sections. Another very important thing to use is USE RELATABLE COLORs. Use colors that look good together. Look up on GOogle for color scheme websites and use those colors (such as these color schemes/swatches: http://aviary.com/halloffame?t=toucan) I've already made many sites, but here's my best work. It's my own flash game website: http://www.flurpal.com
Notice the very apparent gradient in the background - light grey to a lighter gray. This can be done with photoshop obviously. Also the huge heading, and sexy subtitle to the heading - "free flash games". Also, I believe that the gray background, green heading/borders, and light gray text goes together well - it's a "scheme". Good luck!