If we are talking about an average website (blog, e-commerce site, etc.), the homepage is VERY important in terms of SEO. It's usually the main landing page that brings most traffic that's why you cannot simply put some Flash on it, as if it's a Disneyland website :)
The important thing is not to optimize your homepage for the same keywords you optimize your category pages. In other words, you shouldn't target two pages for the same keyword. For example, if all you sell is t-shirts, don't target your home page for the word "t-shirts" and have a category page optimized for "t-shirts". Then, if someone searches for "t-shirts," search engines don't know which page to display, and both of your pages can rank lower.
Instead, try to make sure that your homepage:
- targets your brand name + general product keywords
- includes text/visuals on products/services
- has links to the landing pages and category pages
- helps a user quickly understand what your site's about
- does NOT include any auto-play content (it'll just freaking irritating)
And look at the top-ranking competitors in the niche - see what content strategy they follow and what you can take from that.