Traveling with a baby and want to drive? Here are the major options you might consider (we mostly did #7, a carseat backpack):
No carseats are needed on trains, busses, etc. If you're going somewhere well-connected by public transit (most cities in Europe, New York City, etc.) this can be a great option. On one trip we took our son to the relatively small Italian town of Ortisei, which required 2 trains and a bus, but it worked!
This way you don't need to worry about the carseat in the airport/airplane, but you have one in you rental car—we did this on a couple trips. The downside is that the car rental agency might not have the right thing (there are plenty of horror stories online), and it costs a bit more (although AAA members can skip the charge with Hertz).
Once our son was over 3 years and 30 pounds, we travelled with the RideSafer Vest, which is as safe as a carseat but much more travel-friendly (especially for those of us who don't own a car). He didn't find this very comfortable for long car rides, however (so it's better if you'll only be driving a little bit, like short taxi rides). On the plane you can use the similar CARES (Child Aviation REstraint System), rated for kids 22-44 pounds.
Most airlines let you check a carseat (and a stroller) at the gate at no extra charge
Consider getting a bag to store your carseat, which in theory helps protect it from damage in the luggage compartment
If you bought your child a separate seat on the plane (or they have an extra seat), you can strap most carseats to the airline seat (similar to lap belt installation in a car)—check your carseat beforehand to see if it has a sticker for flight use (more on the Car Seat Lady's page)
Most infant carseats can attach to a stroller, which you can push around the airport (and your destination). For most of our trips, we didn't want to deal with schlepping a stroller around, and in many cases were traveling places with cobblestones and/or stairs where a stroller is a liability, not an asset.
Some folks like the Traveling Toddler (or similar products), which allows you to strap a carseat to your rolling luggage (your kid can even sit in the seat as you push it like a stroller). We didn't travel with wheeled luggage (again due to places with cobblestones/stairs), so this was out for us.
Especially if you have a relatively light carseat (ours is < 10 lbs), you can sling the carseat over your shoulder. However, when we tried this, we found it wasn't comfortable for more than a few hundred yards/meters.
Various companies make backpacks that are sized to carry carseats...they also can double as check-in bags if you gate check your carseat. Two of the best seemed to be the J.L. Childress Ultimate Backpack Padded Car Seat Travel Bag and the ZOHZO Car Seat Travel Bag, but we chose the latter because it looked a little better-made (some Amazon reviewers complained about broken zippers on the Childress). So far we've been happy with the ZOHZO; it was a bit large for our infant carseat (Cybex Aton 2) but it just fit our convertible carseat with its foot retracted (Evenflo SureRide).
All US vehicles manufactured after 1996 have "ratchet" retractor locking modes on seatbelts, and all US vehicles manufactured after 2001 have LATCH (Lower Anchors and Tethers for CHildren)...but other countries have different standards. We had a rental car in Italy, for example, whose seatbelt did not have a "ratchet" locking mode. Get a seatbelt locking clip before you go—Diono makes a popular one (sold in various online stores including Amazon, Bed Bath & Beyond, and Walmart), and some car seat manufacturers will send one on request. Car Seats for the Littles has more info about how to use locking clips here.
More ideas at travelswithbaby.com; more info about carseats and travel at CarseatBlog.com