Don,

Are you looking to purchase current domains or expired ones? I prefer expired domains as the process is faster as the discussions with a current owner can take weeks or months sometimes. You might want to start by getting your feet wet with GoDaddy auctions.

Don, it sounds as if you want to buy a ready to run website off the shelf.
There are three separate things that you need here:
1. A domain name (as in www.example.com)
2. An account with a hosting service who will deliver your site to the internet
3. The actual web pages.

I don't know if there is much of a market in off the shelf sites. Most people would buy a domain and then either build the site themselves or hire somebody to write the content.

I have been saving money and now I'm considering buying websites. What do I need to know? Is it worth it? I'd prefer near-100% automated websites but others would be fine.

Check if the domain name, ip and site itself are clean: no copied content, no red flags on it and no dark things that might get you banned on your aff or AS accounts.

Is is worth it? I think it is but it depends on how you check the options.

Automated sites? don't know what you mean. If you mean automated by using a CMS to admin your content, thats fine, BUT there are many guys out there offering "automated" self updating sites using scripts to scan the web, copy and post copied content. Stay away from that.

I'd prefer near-100% automated websites

If you don't plan on adding original useful content yourself and want that done automatically expect poor results. If you mean automated as in using a content management system to create pages around your articles you've got several solid options.

Is it worth it?

It can be. Don't get taken in by things like pagerank or current traffic details because those can't be purchased, there is no guarantee they will remain the same when you get the site.

What is important is quality content or a quality tool/service.

Checklist:
- Solid descriptive URL's
- Accurate page titles
- Unique high quality original content

The rest is less important when buying but these are what a search engine already knows about.

Page titles can be changed but I rank them as important because they play a huge role in what brings visitors to your site. "10 ways to beat your neighbor at weed pulling" is not as good as "10 weed pulling tips" or even better "weed pulling" or "weed pulling tips".

Why? Because most of those words aren't searched for. "10 ways to" is done to death and "beat your neighbor" is almost about death but neither tells a search engine what the page is about. Current traffic levels can often be a reflection of proper title use, it matters.

The history of earnings is also important. Make sure to ask for the earnings from the last year (with proof). If the earnings are all over the board, you may want to find out why before jumping in.

Just to add it the mix,

If its old websites live websites your buying

1, how old the sites are will play a part.

2, How many links are pointing to the site and how old are the links and what type of links are they naturally back links that will stay in place once you buy the site or are they links that have been paid for or added by the webmasters other sites.

3, What research in terms of stable ranking will you carry out? (even if the content, titles, h1 tags, design and theme of the site stay the same there still risk in terms of losing your ranking)

I would not suggest starting from auction websites. Most of the websites you find here are the "flip" kinds where websites are built with the sole intention of selling them off - not the rightly nurtured site you want to buy with your money.

What I would suggest is pick your niche, browse through hundreds of sites in the niche, find the upcoming ones with great potential and contact the owner directly if they are interested to sell.