I am going on a trip with one memory card; should I buy another or would a USB flash drive be helpful for storing images?
Not to supplement but perhaps to complement.
Assuming you don't shoot like crazy, try to get enough cards for the photo trip. This should be your first copy of all your photos and bringing. Do not offload photos if you do not have to.
Then it makes sense to have an extra backup device. Some people use a computer's hard-drive or an external one (possible inside an iPod or Media-Player), which comes to more or less the same. Your backup will be on a fragile and thief-tempting device.
Using the computer, you can backup to those relatively cheap USB devices which are generally quite durable and easier to hide.
Even better, you can use your computer or an independent burner to copy your memory cards to DVDs. Disks are extremely durable, extremely cheap and virtually no value to anyone but yourself. Normally I burn everything twice, keep one copy with me and mail myself the second copy. Replication and duplication like this greatly improve your chances of not losing anything.
Generally speaking, memory cards and usb storage drives are pretty comparably priced. So the real question is which would you have more use for long term? And will you reliably have any way to transfer images from your memory card onto the USB drive? Usually that's going to require a computer, and well, if you have computer you have a number of other options, such as just storing them on the computer (assuming it's yours) or sending them along to some online storage (assuming the computer has reasonable internet capacity). Or a number of other options Itai lays out.
Personally, in that situation in the past, I voted for the memory card. It was about the same price as a USB flash drive of comparable capacity and speed, but it was far more convenient to just swap from one card to another. (I actually took 2... and still ran out of space and ended up ordering a 3rd from newegg while on the trip, delivered to where I was staying.)
My rule of thumb for a multi-day trip is to use one card or less in a day so that if a memory card dies or is lost I will not lose all of my photos from the trip. It is rare for memory cards to die, but I have had 2 Lexar Pro memory cards corrupt images in the past 3 years. So a 10-day trip would require a minimum of 10 memory cards, my actual number is more like 14 cards because I am shooting RAW and my cards are 4GB each or less.
I do have an external hard drive backup device that copies memory cards but I no longer use it. For most occasions I have a laptop with me and copy all of the images to the laptop each night for backup and a chance to look at the day's photos. But I do not erase/format the memory cards until after I get home and have all of the images backed up and verified.
A USB flash drive is a lot like a memory card except that you can't use it in your camera. They both are small, have limited capacity compared to a hard drive, and are about the same price.
A memory card will be much more useful to you as a photographer than a USB flash drive.
Since you suggested a USB flash drive I assume you are taking a laptop with you anyway (since you certainly can't use a USB flash drive directly from your camera). If this is the case, why would you not just use the laptop itself as storage for the photos once you clear them off your card? And if you need backup, you can invest in a portable hard drive as well. This works out much cheaper per GB and you also get to have a backup.