Doctor Who was not a love at first watching for me. I watched the 2005 season's first few episodes, and was left confused and not overly committed to it. However, BBC-America played a more recent episode featuring Matt Smith as the Doctor, and I found myself utterly hooked. It featured Weeping Angels, creatures who were frozen whenever looked on by a living thing, but deadly killers if you even blinked your eyes. With renewed interest, I set to watching the reboot of 2005 featuring Chris Eccleston as the Doctor, a powerful and ancient timelord who travels through time and space to help the humanity he so desperately wants to be a part of, befriended humans and fighting off creatures along the way. It is both big and epic and simple and silly all at once.
Children and adults love Doctor Who in Great Britain. The love has grown in America as well, with thousands flocking to Comic Con to catch a glimpse of Matt Smith and his human companions. If you are a Doctor Who newbie, I'd recommend starting with Season 5 of the reboot, which is when Matt Smith takes over as the Doctor. It is rather self-contained and easy to pick up from there. If you become hooked, go back to Eccleston and Tennant, or even further back. The Doctor travels through space and time in the Tardis, a spaceship shaped like an old-school police box. It is, as the show loves to point out, "bigger on the inside." I'd argue that the show itself is much, much bigger on the inside.
Check out the trailer for Season 5 here.