The most common Broadband Internet access or high-speed Internet are DSL and Cable modem. The futur, already available for some, is Fiber Optics in the Home.

• DSL (Digital Subscriber Line):

You basically have main 2 types of DSL: ADSL (Asynchronous-DSL) and SDSL (Symmetrical-DSL).
With SDSL downloads and uploads speeds are the same. With ADSL the the upload speed is slower the the download speed (this is fine for most internet users), since we tend to download a lot more then we upload.

The DSL speed with depend on the service you purchase. DSL providers usually will charge higher prices for higher speeds. Your distance to the "central office" (CO) might limit the speed you can actually get. In some case you can be so far from the central office (1¼ miles+), that DSL will not be reliable. I experienced this in Colorado and had to switch to cable-modem. Usually speed will range from 256kb/s to 1Mb/s. Lately we are seeing more and more variant of DSL. Like ADSL2+ which can deliver up to 24 Mb/s.

When using DSL and you main phone line, you will have to install filter (provided by the ISP in most cases).
You will also often here, from people selling DSL,  that DSL is a dedicated line. This is true, in the sense that, from your home to the central office. your connection is on a dedicated physical cable. But once at the central office you use the same connection then all other DSL customers. So this is really more of a marketing selling point then a real difference. In fact most often cable-modem is faster then DSL.

• Cable modem:

Cable modem is usually faster then DSL. Speeds range from 640kb/s to 7Mb/s (and more). With cable-modem all the home of a neighborhood share the same physical cable. If you are in a neighborhoods were many people tend to download large file you could experience slower speeds then usually. In other words the speed can vary based on how heavily your neighbors use the cable-modem connections.

Cable modem speed are capped (since the actual speed permitted by the physical coaxial cable is a lot more then what cable-modem providers offer).
For details see: http://en.wikipedia.org/wiki/Uncapping

• Fiber Optics or Fiber To The Home (FTTH):

This is the future of the internet. Some lucky ones can already get this service in the United States. Fiber Optics is basically a fiber (think glass) that conducts light Yes think speed of light. Initially FTTH will offer speeds up to to 100Mb/s but will be able to grow with time. FTTH is far superior then any previous technologies and will permit Internet, TV and more on the same cable and still have room for more services in the coming decades.