I have a site that is listed in the supplemental index in Google. I've decided it's finally time to do something about it, but I get varying pieces of advice from people, and in the end it seems no-one really knows what has happened.

So can anyone help me out, and let me know what I need to do?

Theories so far:
1) All my meta tags, and page titles are the same (site was built using a template)
2) I have lots of content from the encyclopedia Brittanica
3) The site is in the "sandbox"
4) I did something that's been viewed as spammy
5) I don't have enough inbound links
6) Only Google knows the answer.
7) All of the above

well, I know I need to deal with 1), but this is more of an SEO thing and would not lead things to being supplemental so I'm told. The 2) should only affect the pages where there is duplicated text if this was the problem. 3) the site is 2 years old, and IS listed in Google. 4) Maybe, as I used to have some random link exchanges in the past, but these have since been removed (Google still has the old link pages in their cache though). 5) this would only effect ranking surely, and have nothing to do with being listed as supplemental. 6) Probably, but as they don't answer questions like this not much help. 7) it may well that the effect is amplified because of a number of things I've done wrong.

Any help would be very gratefully received.

If you have duplicate content on your site, and it seems from your post that you do, it will stay supplemental forever. It is possible that if you have enough duplicate content all of your content will go supplemental. Can't confirm that but it is possible. Google just made a good blog post today about duplicate content. I suggest reading it.

FYI, there are virtually no confirmed facts about the supplemental index so you won't get a definitive answer from anybody. Only guesses and conjecture.

There's been all this talk about the supplemental index recently. How on earth do you tell how many pages, if any, you have in the supplemental index?

do a "site:www.aspectart.com" search in Google. The non-supplemental sites are listed first, so if you count them then minus it from the total pages listed that should get you your count. Or if you have very few listed as supplemental just go to the last few pages and count them manually.

Maybe someone has written a little program to do it for you already.

As you will see from my site - EVERYTHING apart from the home page is supplemental.

Ah, I see. However, have you noticed any incoming traffic from the google results? Does google ever point visitors to pages other than your homepage?

I get traffic from Google's supplemental index and the pages are all inner pages of my site. Most of the traffic I get from search engines are to my inner pages.

Yes, you might help the cause by giving the pages more prominence via moving them closer to root -- but still, if they don't have any inbound links, there's no guarantee you'll get out.

Inbound links from inner pages do help. They just need to pass enough PR which means they need inbound links themselves.

Google's official word is that the supplemental index doesn't affect your page rank. However I've heard that having your website in the supplemental index does at least affect the frequency with which your site is 'cached'.
My site is also in the supplemental index and doesn't get a lot of hits:
<snip>

A keyword rich, sitewide meta description is the best way to have your entire site wiped off the SERPs for dupe content, or bunged into the supplemental index.

http://www.ragepank.com/articles/43/duplicate-content/ explains how a sitewide meta description can screw you over big time.

Supplemental pages are not unique looking enough, or don't have enough links. If you have a dynamic site, it's easy to have thousands of pages that aren't particularly unique looking. If you have 1000 low-value pages, and only 50 high-value pages, google may just say "Bah, too hard" and chuck the whole lot into the supplemental index.
My advice is to block Googlebot from seeing the low value pages via robots.txt, rel=nofollow or meta noindex. This increases the signal to noise ratio on your site. Hopefully Google will remove your rubbish looking pages and add the good pages to the main index. Once this happens, see what you can do to make your rubbish pages look less rubbish, and get them indexed again.

I had a real problem with machine generated pages going supplemental, because they looked too machine generated. The solution was to add a few sentences of unique content to the top of each page, and it works. I chip away at it by fixing a couple of records per day. If you are suffering from uniqueness, nothing works like hand-written content.