1. While Craigslist is a valuable resource, make sure you follow Hack #4 and #5 - there are a lot of sleazy individuals who will pass salvage title or otherwise garbage vehicles. I would add one other note to that recommendation - search via the 'by owner' listings vs the 'by dealer' ones. That cuts down some (but not all) of the buy here/pay here trash-lot stuff. Searching for larger dealer vehicles can be done via something like autotempest (which also conducts Craigslist searches too)
2. While buying via Craigslist is generally easy and definitely recommended in many situations, selling can sometimes be a complete PITA. Dumping the car at CarMax can work as well in that case. You take a bit of a hit on the sale price, but its generally less in my experience than trading it in.
3. Sometimes there is a damn good reason why Luxury cars have taken an appreciation hit. Make sure you factor in scheduled and unscheduled maintenance with your purchase plans. Some luxury brands (Lexus, some Infiniti, Acura) are easier to maintain than others, but they inconveniently don't seem to depreciate quite as much. One thing I would add here too is - If you don't care about your image too much, look into 'old people's' cars. Things like the Cadillac DTS, Lincoln, Mercury Grand Marquis, etc... Because they are so unfashionable, the depreciation hit on them is HUGE, and you can really get decent, comfortable transportation for cheap. The gas mileage might not be as good as a Toyota, but $5k in savings can buy a lot of gas...
4. Carfax is important, but its not foolproof, and its no substitute for a good mechanic's inspection. What I look for is a gap-free history with no dramatic changes in mileage, and no record of fleet ownership. Why no fleet ownership? Have you ever abused a rental car, or known somebody who has? I would never buy an ex-rental, and would have a hard time looking at other ex-fleet sale cars - the incentive for responsible ownership is very often not there, even if scheduled maintenance may have been more rigorously followed.
5. In some cities there are 'Lemon Buster' services that can travel to the dealer/owner and inspect the car on-site. YMMV of course, but I have found them to be pretty useful and inexpensive. They also give you a nice inspection report that can be used as negotiation leverage.
Additional points to make:
Financing - unless you are a very savvy negotiator, I would NOT recommend dealer financing over bank/Credit Union financing (especially CU.) Financing/Dealer Fees are a huge source of income for dealers, and they typically have some real hard-asses stationed at the financing desk. Much easier to just pay with cash from the CU or your pocket. Paying ahead, by saving money for your next car instead of making payments for the current one is a very savvy move if you can get away with it.
Used car prices are highly localized. Where I live (Austin TX,) I have found that 2-5 yr old used cars are typically about $1k more expensive than cars in larger Texas cities like Houston and Dallas. Make sure your internet searching takes this sort of variance into account. If you save $1-2k on the price, a $150 one-way plane ticket is pretty cheap. For those in the rust belt, I would not even bother with buying used vehicles past a certain age locally - why take the chance on hidden rust issues?
Rule of thumb for used car purchases - there are always more cars! Don't EVER think that the car you are looking at is a special flower and that you will never find one that's the same. ALWAYS reserve the option to walk away. I personally walk-away from most cars I look at. Don't like the lot/seller? Walk away. Not getting a good feeling from the car? Walk away. There are always other options.
Finally, I recommend the book 'Don't Get Taken Every Time' by Remar Sutton. Tons of good info on how to avoid some obvious pitfalls for both used and new car purchasing.