Off the top of my head, I can think of 16 different types of non-academic science jobs I have friends doing with their PhDs.
1. Staff scientist at a National Lab (i.e. my former life). See posts here, here, and here. This type of position is very much like a professor at a research intensive university.
2. Research scientist in industry. Very, very hard to find now that most of the really big corporate labs have shut down. Companies that I know that still have them are in the semiconductor, chemical, pharmaceutical, computer, defense, consumer product, and materials industries though. In startup companies, it is not uncommon for people to be hired to do some research and some other stuff "on the side".
3. Translation engineer (called lots of different things at different companies): A cross-discipline team of scientists and engineers who take discoveries made by more basic researchers and bring them to pilot plants and/or production plants for use in actual products. This one sounds like a really fun job to me. A friend of mine has been doing it for 8+ years and loves it.
4. Application scientist/engineer: I am mostly familiar with this for scientific instrumentation companies. I know 3 or 4 people who do this, and really like it. They spend some fraction of their time supporting researchers (mostly troubleshooting and installing top end systems, but some figuring out how to get their instruments to do specific new tricks requested by customers) and some fraction of their time developing new methods on their instruments and/or improving the instrumentation for the next product iteration. A great job for someone who loves tinkering with equipment. Applications scientists/engineers are the people you talk to when you call a company for technical assistance.
5. Software developer or designer: We use a lot of instrumentation and computation in my research sub-field, so I know a few people who moved into this full time after completing their PhDs. One friend works for a general software development place after doing a computational dissertation on software optimization. Another works for a scientific instrumentation company on their analysis software.
6. Science writer: One of my former classmates is a freelance technical writer/science journalist. The journalism pay sucks, but he finds it more fun. The technical writing pays really, really well (and requires an advanced degree).
7. Program officer at a funding agency: I know 2 people doing this--one left National Lab to become an officer because he wanted to move away from doing research himself. The other started at Booz-Allen as a consultant supporting DARPA after her postdoc, and then liked it so much that she became a program manager herself. Both had extensive research experience prior to becoming a PO. Postdocs are DEFINITELY required for this type of position, and more experience is a big plus so that the POs are familiar with lots of different research environments (where their programs will be carried out).
8. Patent officer: You don't need a PhD for this (a MS is enough I think), but the pay is much better if you have one. You evaluate patents for the US patent office. Sounds really boring to me, but the pay and benefits are excellent.
9. Patent attorney: I know two well--one from my grad school and one from my postdoc. Both got hired by law firms, who then sent them to law school while they worked. A grueling schedule, but they have no law school debt. Again, not something I am really into, but they seem to like the excitement of seeing so much technology on the cutting edge.
10. Contract scientist: The US government hires lots of these. There were quite a few at National Lab. It is a pretty nice job--you get security and benefits from the company, and you get to change projects fairly often so you don't get bored. The most famous of these is SAIC.
11. Science/technology consulting: Booz-Allen is the one I am most familiar with, but there must be others. DARPA uses them to support their POs. My friend who worked there said it was a good job--interesting work, good pay, and interesting opportunities. She organized meetings for her PO (and not just program reviews--she also set up and ran mini-symposia with the leading researchers in the relevant field), went to tons of conferences to keep her PO abreast of new developments in his area, helped screen proposals, helped design calls for proposals, and basically provided technical expertise for her PO to draw on. Required a lot of travel, though.
12. Sales: Scientific equipment sales often requires a PhD. I know one person doing this, and he likes it, because he LOVES talking to people and meeting new people. Requires extensive knowledge of the techniques possible with the equipment to be sold. If you've ever seen a PI buying instrumentation (particularly the stuff worth $75k+), the sales people probably had PhDs so they can actually talk about the experiments with future customers.
13. Formulations scientist/engineer: many products (like medicines, food, coatings, and personal care products) are a mix of active and inactive ingredients. The formulations team designs the final formula to get the best activity profile for the active ingredients while also obtaining desirable color, feel, taste, texture, etc. They also aim for the best cost/most environmentally friendly/best processibility possible. Lots of physical science and characterization is involved (outside of the synthetic parts).
14. Quality control: In lots of industries, PhD level positions set up and modify the procedures that will be used for quality monitoring. A friend does this for a particular industry using the instrument we used as a workhorse in our PhD research. He selects the brand, type, and models for the instrumentation to be used worldwide by his company, establishes what tests will be done at what points in the manufacturing process, establishes the pass/fail criteria, and develops training protocols so that the same tests can be carried out of different facilities worldwide with the same results. To do this, he must keep up with the latest and greatest in technology changes (which is really fun), and occasionally gets patents and/or papers (depending on which departments he is working with).
15. Defense contract work: The big ones hire scientists and engineers with lots of different backgrounds to make sure they can develop their huge programs from start to finish. I only know two people who do this type of work. One is a designer who works on a tiny piece of a huge project (think designing the landing gear on a new plane). The other specializes in coatings, and helps decide what coatings will be used for various products and how they will put the coating on the final object.
16. Entrepreneur: I know a guy who licensed IP from his PhD research on very favorable terms from his University. He set up a small company selling a niche scientific products for research labs that is now doing quite well. Requires access to some capital, and massive risk tolerance (so I would never have done this), but he seems happy. Before starting his company, he worked for a year as a PhD-level sales person in a company selling related products to learn more about how it all worked.
UPDATED: Fixed grammatical and spelling errors that annoyed me.