The first thing to prevent bots from stealing your data is not technological, it's legal. First, make sure you have the right language in your site's Terms of Use that what you're trying to prevent is actually disallowed and defensible from a legal standpoint. Second, make sure you design your technical strategy with legal issues in mind. For example, in the US, if you put data behind an authentication barrier and an attacker steals it, it's likely a violation of the DMCA law. Third, find a lawyer who can advise you on IP and DMCA issues... nice folks on StackOverflow aren't enough. :-)
Now, about the technology:
A reasonable solution is to require that users be authenticated before they can get access to your sensitive Ajax calls. This allows you to simply monitor per-user usage of your Ajax calls and (manually or automatically) cancel the account of any user who makes too many requests in a particular time period. (or too many total requests, if you're trying to defend against a trickle approach).
This approach of course is vulnerable to sophisticated bots who automatically sign up new "users", but with a reasonably good CAPTCHA implementation, it's quite hard to build this kind of bot. (see "circumvention" section at http://en.wikipedia.org/wiki/CAPTCHA)
If you are trying to protect public data (no authentication) then your options are much more limited. As other answers noted, you can try IP-address-based limits (and run afoul of large corporate proxy users) but sophisticated attackers can get around this by distributing the load. There's also likley sophisticated software which watches things like request timing, request patterns, etc. and tries to spot bots. Poker sites, for example, spend a lot of time on this. But don't expect these kinds of systems to be cheap. One easy thing you can do is to mine your web logs (e.g. using Splunk) and find the top N IP addresses hitting your site, and then do a reverse-IP lookup on them. Some will be legitimate corporate or ISP proxies. But if you recognize a compeitor's domain name among the list, you can block their domain or follow up with your lawyers.
In addition to pre-theft defense, you might also want to think about inserting a "honey pot": deliberately fake information that you can track later. This is how, for example, maps manufacturers catch plaigarism: they insert a fake street in their maps and see which other maps show the same fake street. While this doesn't prevent determined folks from sucking out all your data, it does let you find out later who's re-using your data. This can be done by embedding unique text strings in your text output, and then searching for those strings on Google later (assuming your data is re-usable on another public website). If your data is HTML or images, you can include an image which points back to your site, and you can track who is downloading it, and look for patterns you can use to bust the freeloaders.
Note that the javascript encryption approach noted in one of the other answers won't work for non-authenticated sessions-- an attacker can simply download the javascript and run it just like a regular browser would. Moral of the story: public data is essentially indefensible. If you want to keep data protected, put it behind an authentication barrier.
This is obvious, but if your data is publicly searchable by search engines, you'll both need a non-AJAX solution for them (Google won't read your ajax data!) and you'll want to mark those pages NOARCHIVE so your data doesn't show up in Google's cache. You'll also probably want a white list of search engine crawler IP addreses which you allow into your search-engine-crawlable pages (you can work with Google, Bing, Yahoo, etc. to get these), otherwise malicious bots could simply impersonate Google and get your data.
In conclusion, I want to echo @kdgregory above: make sure that the threat is real enough that it's worth the effort required. Many companies overestimate the interest that other people (both legitimate customers and nefarious actors) have in their business. It might be that yours is an oddball case where you have particularly important data, it's particularly valuable to obtain, it must be publicly accessible without authentication, and your legal recourses will be limited if someone steals your data. But all those together is admittedly an unusual case.
P.S. - another way to think about this problem which may or may not apply in your case. Sometimes it's easier to change how your data works which obviates securing it. For example, can you tie your data in some way to a service on your site so that the data isn't very useful unless it's being used in conjunction with your code. Or can you embed advertising in it, so that wherever it's shown you get paid? And so on. I don't know if any of these mitigations apply to your case, but many businesses have found ways to give stuff away for free on the Internet (and encourage rather than prevent wide re-distribution) and still make money, so a hybrid free/pay strategy may (or may not) be possible in your case.