What kind of jobs would people with a doctorate in linguistics get?

I'm not necessarily in a position to talk about all kinds of jobs, but I can at least tell you what I've been doing as someone with a doctorate in linguistics!

I was teaching for a while, but (fair warning) teaching positions are hard to come by, especially in a field like linguistics where you're not going to find the same demand as there would be for, say, math and English and history professors. (Everyone has a math department. Linguistics departments are harder to find.)

What I've been doing for the last six or seven years is programming. Lest that sound like a generic fallback position, though: my job title is "Senior Linguistics Developer", and much of the work I do is centered around natural language processing. I'm not writing parsers from scratch, but with a background in linguistics--even theoretical, rather than applied or computational, linguistics--I'm able to evaluate parsers that exist and adapt them to my company's needs. Some parsers, for instance, will simply mark "not" or "never" as adverbs; they're not wrong, but any company doing anything that involves understanding language will need a more nuanced understanding of how negation works. Some of this work, then, is geared towards particular languages; some of it is saying, "Given how languages work, what do we want to do with the information we get from parsing the text?".

As I said, I can't necessarily talk about what other jobs might be available more generally. But I know that a lot of companies--many of them here in Massachusetts--are doing work with computers and language. They range from large ones, like Google and Facebook, all the way down to three-person startups looking for someone to improve their ability to automatically understand customer input. And, as I said, I'm not writing the software to parse things myself; but there are companies that are, and they certainly always need people who not only speak some particular language but who understand how that language works. Even if computers aren't your thing, many of these companies will be filling other positions--sales people, people to oversee the work, QA testers, what have you--where an understanding of linguistics will be at least helpful, maybe even essential.

It's not a complete answer, but hopefully it'll give you some sense of what kinds of jobs are out there!

The area of application of linguistics is very broad. The major thing that you need to do is to determine which application might be best for you to pursue. Selecting a career area is like buying a pair of shoes. The may look great and have many varieties, but you need to first find your correct size and then try on the variety of options to determine what might best be suited for you. During my many years in Human Resources and College Recruiting, I have developed these steps that have helped many to end up in a career situation that was most productive and comfortable.