To understand why I love the TARDIS, I need to address it's core concept, time and space travel combined.
Although time travel is inherently fictional, it has been a heavily written about subject. I think the first time I saw time travel was in Back to the Future. Although I must say The Terminator and T2 are all time favorite time travel movies of mine as well. The idea that you could travel in time and nudge your own life into shape, almost sculpt it, is fascinating to me.
Now, when you take the concept of time travel and you add the dimension of space, I think that officially brings the entire idea into an exceptionally fantastic place. Time travel and space travel put together, truly stretching the limits of the human mind. You can now travel anywhere, absolutely anywhere. Although your personal time line travels one way, you may create that path any way you like.
Doctor Who is acted with such conviction that it is truly moving and when you add the fact that absolutely anything is possible, well, the entire thing is amazing. It's an amazing concept.
The TARDIS is the vessel that carries that entire concept. The TARDIS is amazing, right?? It is alive, it knows the Doctor, it knows the time lords, it knows Gallifrey, it has a heart, it's blue, and it can do anything and go anywhere. Plus it has that shield that can hold off Dalek blasters, which has definitely come in handy. I also love whenever he lands it and the door faces a wall so he has to move it. I love that it took human form and interacted with the Doctor. Think about that meeting, then think about the wonderful Beatles undertone. When the Doctor things she wanted to say "Goodbye", but she really wanted to say "Hello." "You say goodbye and I say hello. Hello, Hello! I don't know why you say goodbye, I say hello!" I really feel like that little part is a Beatles tribute. They've worked in fantastic obvious music references in other episodes. Like the Flesh episodes where they constantly say "Us and Them", such a Pink Floyd reference.
The TARDIS rewards the Doctor and guides him on his entire journey to help and save worlds in danger. It is absolutely as important as the Doctor himself.
So, yeah, that's why I love the TARDIS :-)