All .coms are taken, but not all 3 letter domains. Nondotcom domains are not worth as much (some are only worth the reg fee depnding on letters/numbers). http://www.3la.org/ has a list of available 3 character .com (none), .net (several hundred), and .org (several thousand). Some of them may be taken, but if it is not on the list it is almost certainly taken. Of course, most of the available ones are worth only the reg fee at this time. There is no comprehensive list that I know of that lists taken 3 character domains that are for sale. But http://www.3character.com has links to several resources.
All of the 3 letter domains are taken, and when they expire they are grabbed up the instant they are let go by ICANN by places like Pool and Enom and get bidded on.
Not all three letter domains are taken. All three letter domains of any value are taken. (example: xfg.name is available). The OP did not specify what TLD.
What exactly do you mean by 'active' domains? Do you mean the ones that have sites on it or the ones that are registered???
Doing a random sampling of 20 of the domains, I got about 50% not registered. Of the .net domains I tested, 1 in 6 were still available. The .org domains seemed much more accurate. Of course, I could have just been lucky. My point though, was that if a person wanted to register (as opposed to purchasing from somebody that owned one) a 3 char domain, it would be much quicker to look for ones from that list than to check them all.
The only LLL available I believe are the .name ones and those aren't fetching any money. The highest a LLL.name has sold for according to namebio.com is $300 and that was for wap.name.
Don't waste you're money with LLL.name domains, the .name extention is the crappiest extention out there