High speed. Haven't had dialup for more then ten years. Seriously, there still are people on dialup in the west world?
People in rural areas (at least in the US) often have a difficult time finding quality broadband connections. My uncle, for example, lives five miles away from the center a town with 35,000 people. His best wired option is ISDN (which can hardly be classified as high speed at 128kbps). The wireless options he has, microwave or satellite, are both expensive and and slow. He opted for microwave, and gets somewhere in the neighborhood of 1Mbps per second -- which I still think is very slow -- and which costs him close to $100/month.
The damnedest thing is that, should he move just one mile closer to the town center, he'd have cable, DSL, and even some fiber options to choose from. But none of those companies will run a backbone through his area. He's waiting for Wi-Fi services to roll out eventually.
For me, I have an 18mbps fiber connection from AT&T UVERSE. I have to say, I've always despised AT&T -- even the broken bells with which I've worked over the years -- but UVERSE is easily the best Internet I've ever had. Even though I've had technically faster connections, UVERSE has the lowest latency and highest stability of any service I know. I've been nothing but thrilled (and surprised).
ETA: I forgot to mention that I am a relatively heavy user. I telecommute via the Internet, my voice service is through Skype, I'm often transferring many large media files to and from my company's DropBox, conducting screencasts and/or video conferences with clients and colleagues, and more. While my day-to-day usage may vary, my average monthly usage is somewhere in the neighborhood of 200GB.