My quick rundown:
Title tag: Yes, this one’s a biggie. All indications are that the title of the page matters a lot to Google and the other SEs. Every page on a web site should have well-written title that accurately summarizes the page’s main focus.
Description meta tag: Yes, it matters, in a sense. See here.
Keywords meta tag: No. Google ignores it. I’ve seen evidence that Yahoo finds misspelled words in there, but that’s about it. I use it, because it can be useful during development to help me focus on the keywords that should be on that page. Plus if it ever does become useful, all the sites I’ve developed will already have it. It doesn’t hurt, unless you use it for keyword stuffing.
Headlines and subheads: Yes. There’s evidence that headings and subheads are given more weight by the search engines when they’re enclosed in appropriate heading tags (i.e., h1, h2, etc.). Using a page’s primary keywords in well-written headings and subheadings semantically correct header tags also has the advantage that visitors frequently scan a page, and they’ll see your most important keywords in the headings. And the headings don’t have to be big and ugly: there’s no SE penalty for using CSS to style the headings so that they complement the design of the site.
Image alt text: I don’t believe that alt text in any old image makes much, if any, difference to the search engines. But it’s likely that appropriate alt text in images that are used as links are seen by the SEs as the anchor text for those links. The alt text likely doesn’t carry as much weight in SE rankings as real text links, though; it’s too easy to abuse. It’s a good to include alt text anyway, to help ensure the site is accessible.
Valid code: Not important per se to the search engines, but important for other reasons. Invalid code could interfere with search engine indexing if it’s so badly malformed that the search engine bots simply can’t parse the page.
Bold/strong: In two of his videos, Matt Cutts specifically mentioned the bold and strong tags. The exact wording of his statements suggests that text enclosed in bold and strong tags are likely to carry more weight for ranking purposes.
External links (links to other sites): I dunno. I’ve seen plausible arguments on both sides. If external links help, they probably don’t help much, because anyone can plaster their scraper site/MFA site with links to authority sites. My own opinion? I think that if the sites being linked to are quality sites, and if other signals of quality are present, that external links can help. We know that external links to “bad neighborhoods” can hurt, Matt Cutts has told us that in so many words. My recommendation: If the external link is good for your visitors, go ahead and include it.
Keyword density: No. Well, sort of. There’s no definitive percentage of keyword density, no magic bullet. But logic tells us that overdoing it will end up making a page feel spammy. And unless you’re Adobe or George Bush, it’s probably impossible for a page on your site to rank well for a keyword or phrase unless that keyword or phrase appears somewhere on the page. My advice: Do the keyword research, then write for your users. If your writing is on topic, the keywords will put themselves where they belong, for the most part.
Good content: Yes, yes, and yes again. Valuable, well-written text that gives your users what they’re looking for, whether it’s a specific product and product specifications, or the history of the blue widget. In the long haul, there’s no substitute.