Tangentially, and pardon my ignorance, I'm not a biker: I can't understand people who shell out thousands of dollars for a bike, are these so much better than a $500 one?
As many other answers say, yes, there is a difference.
Here are some details (for 'racing' road bikes, which I know best):
For around $400, if you buy well online you can get something with an aluminium frame, carbon fibre fork and moderately decent components (eg [1]). It'll probably weigh a bit under 30 pounds (13 kg).
For around $700 you'll get a bike with similar specs from a major manufacturer and you can get it from a bike shop, where they will assemble it for you, make sure you get the right size etc. See [2][3]
For around $1000 you can get a carbon fibre frame on your bike (online, with terrible components[4]) or bikes from major manufactures where the components start getting better (eg Shimano Sora 9 speed). These bikes should be between 20 and 25 pounds. See [5]
At $1500 you get bikes from major manufactures that are suitable for racing (ie, Shimano 105 10 speed, eg [6]), or can get pretty good carbon fiber bikes online. You also start getting decent bikes from high end manufactures (Bianchi, Pinarello, BMC). Most of these bikes will weigh a bit more than 20 pounds (9 kg), but if you choose carefully you might get under that.
Over $2000 you get carbon frames and Shimano's second to top component set, better wheels, and began getting under 20 pounds more often. High end only manufactures (Cervello, Ridley etc) are making their base level bikes.
Around $5000 you start getting electronic shifting, or better aero frames, deep rims on your wheels. You can start considering custom made frames. Your bike should weigh well under 20 pounds, and you can probably get down to the UCI limit of 6kg.
At $10,000 you are getting bike similar to what they ride in the Tour de France. You can get a power meter built into your crankset or wheels. The carbon frameset has been wind tunnel tested and is engineered so carefully that some parts of your frame only have a single layer of carbon, yet you still can't flex the frame at the bottom bracket. You probably have to add things like the power meter as ballast to make sure you are over the UCU weight limit. You can consider custom titanium[7] or trying to buy onto the speedvagen waiting list[8].
Or, if you're me, you're often carrying 20 pounds of stuff in a backpack on your back anyway, which probably obviates the 5 pound difference in bike weight. I'm riding a Big Buzz: http://www.rei.com/product/775488/novara-big-buzz-bike , which is apparently "sold out" right now, and it seems to work tolerable well. I've ridden friends' expensive bikes, and most of them don't seem to be worth it unless you're racing or riding a LOT of miles.
As many other answers say, yes, there is a difference.
Here are some details (for 'racing' road bikes, which I know best):
For around $400, if you buy well online you can get something with an aluminium frame, carbon fibre fork and moderately decent components (eg [1]). It'll probably weigh a bit under 30 pounds (13 kg).
For around $700 you'll get a bike with similar specs from a major manufacturer and you can get it from a bike shop, where they will assemble it for you, make sure you get the right size etc. See [2][3]
For around $1000 you can get a carbon fibre frame on your bike (online, with terrible components[4]) or bikes from major manufactures where the components start getting better (eg Shimano Sora 9 speed). These bikes should be between 20 and 25 pounds. See [5]
At $1500 you get bikes from major manufactures that are suitable for racing (ie, Shimano 105 10 speed, eg [6]), or can get pretty good carbon fiber bikes online. You also start getting decent bikes from high end manufactures (Bianchi, Pinarello, BMC). Most of these bikes will weigh a bit more than 20 pounds (9 kg), but if you choose carefully you might get under that.
Over $2000 you get carbon frames and Shimano's second to top component set, better wheels, and began getting under 20 pounds more often. High end only manufactures (Cervello, Ridley etc) are making their base level bikes.
Around $5000 you start getting electronic shifting, or better aero frames, deep rims on your wheels. You can start considering custom made frames. Your bike should weigh well under 20 pounds, and you can probably get down to the UCI limit of 6kg.
At $10,000 you are getting bike similar to what they ride in the Tour de France. You can get a power meter built into your crankset or wheels. The carbon frameset has been wind tunnel tested and is engineered so carefully that some parts of your frame only have a single layer of carbon, yet you still can't flex the frame at the bottom bracket. You probably have to add things like the power meter as ballast to make sure you are over the UCU weight limit. You can consider custom titanium[7] or trying to buy onto the speedvagen waiting list[8].
Over $10,000: McLaren + Specalized: http://www.bikerumor.com/2011/03/17/specialized-mclaren-veng... (actually, to be fair there are plenty of ways to spend $10K+ on a road bike. This is just one).
[1] http://www.bikesdirect.com/products/windsor/wellington3_IX.h...
[2] http://www.giant-bicycles.com/en-us/bikes/model/defy.5/9014/...
[3] http://www.trekbikes.com/us/en/bikes/road/sport/1_series/
[4] http://www.bikesdirect.com/products/fuji/fuji_sl3.htm
[5] http://www.specialized.com/us/en/bikes/road/allez/allezsport...
[6] http://www.trekbikes.com/us/en/bikes/road/sport/madone_2_ser...
[7] http://www.baumcycles.com/bikes/romano
[8] http://www.adecadentexistence.com/?p=469