How much of a difference does haivng a great design to just having a neat-looking design make when trying to get links? Except for verticals such as cars, jewlrey, etc. (where having a flashy design is a non-brainer) does it have an effect on link request success rates?

Look is never as important as quality content and the appearance of knowledge etc.

Glad to see you agree! Would you really say "never", though? If you're working with a site that's selling jewlrey or cars or other high-ticket items, is it not really important that they get a professional looking(maybe even fancy..in the case of jewlrey) design? just curious, because you might have worked with a site or two like that before ;)

i think the appearance of the site is not that important to gain more links from other site