If you are going on any extended trip outside of the U.S. you will want to invest in a hiking backpack. Or always pay to have a taxi drive you straight from the train station/airport to your hotel. Also, if you can afford a hotel and taxi and that sounds like typical travel plans for you, then you can stop reading now and enjoy the luxury of your wheeled bag (and probably first class plane ticket, too.)
For the rest of us, we become pack mules for our trips. Backpacks are extremely portable, can somewhat be easily maneuvered on public transportation and free up your hands to snap photos or read a map while you walk to your destination.
The main thing to consider when selecting one is size. If you are going to be flying on a budget airline at all during your trip, you will want to measure your bag extremely carefully before purchasing it. (All of these bags are on the edge of the limits, but reviewers said they traveled overseas with no hassle.) Trust me, European budget airlines have smaller overhead bin size requirements than the U.S. and just because an American airline lets you through, doesn't mean EasyJet and RyanAir will. They will laugh in your face and smile as they charge you an extra 50 euros to check your bag to your final destination. Not that I experienced this or anything.
The money I saved by borrowing a friends backpack was lost (and then some) in two extra baggage fees that I encountered. Lesson learned and hopefully I can save at least one other person from making the same mistake.
Also unlike me, if the top of the bag is taller than your head, then it is too big for your frame. Period. End of statement.
For those of you who will strictly be sticking to travel by train or rental car, then this is not as much of a concern for you because you will be able to check one bag free on most international flights to and from home.
Other things to consider besides size:
1. Extra pockets One giant dump-all compartment will not cut it unless you want to unpack and then repack your bag every night because your toothbrush or charger always seems to end up at the bottom. Bonus if you can find a bag with a pocket on the waist strap to hold money and train tickets.
2. Waist strap Your Jansport backpack might have carried 50 lbs of weight in high school textbooks the ten minute walk from the bus stop to your house, but it will not make the grade in weeks-long travel. Look for a bag with a hip belt so the majority of the weight will be shifted off your back and onto your hips. Your chiropractor will thank you for this when you return.
3. Water bottle holder This is why it's great to get a bag made for the outdoors. I always had a water bottle with me and would refill it whenever I found a water fountain. This is one less thing to worry about holding and you don't have to worry about leaks if you put it inside your bag.
Once you select a bag, it is a whole different discussion on what to fill it with and how to pack it correctly. I'll save that for later maybe.