- What type of bike do you have? Does it have braze-ons for racks?
If not, a trailer is your best bet. (I know, you're right - there are some racks that attach to your seat post, but I don't think those racks can handle too much weight!) - What type of trip are you taking? A "credit card tour" where you're carrying a minimum amount of gear? A fully loaded camping trip? Somewhere in between?
The amount of stuff you need to carry for your trip can help make the decision. For a fully loaded camping trip, I'm much happier with a trailer because it pulls all of the weight off of the bike, and it doesn't change the feeling of your bicycle. If your bike is loaded down with the amount of gear you need (clothing, camping gear, etc.) stored in panniers, the handling / feeling of the bike is very different. But if you're planning a credit-card tour where you plan to carry minimal gear, then you should be able to fit everything in two partially full panniers, which won't have as big of an impact.
If you're planning a credit card tour but you're dealing with a wide range of weather conditions, you still may need a lot of stuff. And if you're planning to camp and you expect flawless weather you might decide to go with something much lighter than your 3-season tent & sleeping bag, so you might be able to pack with much less weight & space. - Are you doing a one-way trip where you have to transport all of your gear by some method other than biking?
Sometimes in this case panniers will win out because you don't have an extra big thing to transport home or to the trip start - and you don't have to worry about excess baggage charges on an additional item. After all, you're probably already paying a fee for your bike!
Of course, if you're traveling on a Bike Friday like I did last summer, the trailer still wins - because the trailer is really the bike case with wheels attached to it. I didn't have to worry about how to get the bike home because I could take my gear out of the trailer and throw it into a duffle bag, then fold up the bike and put it in the case / trailer. All ready to fly... - Do you love the way a bike looks with panniers and hate the looks of trailers? Or the reverse?
Handling concerns apart, aesthetics are important. If you absolutely hate the look of a bike with panniers, then use a trailer. And if you hate the look of a bike with a trailer, use panniers. I'd use this as a last resort for driving your decision though, because there really is a difference in the handling of the bicycle, and to me that is more important than how the bicycle looks.
Keep reading for more specifics...