I think, ignoring any artistic discussion, 30p is what you need for internet hosting, what the majority of us are interested in. I'm not sure if Vimeo/Youtube will even take 24p, but I know for sure it doesn't take 60p. You can upload a 60i video, but it looks horrible with lots of heavy combing.
It seems to me, that most digital still cameras that take video (P&S or DSLR) tend to shoot 30p, maybe with the option of 24p. Camcorders, tend to shoot 60i, though the option for 24/30p is becoming more prevalent. But you have to pay attention because some advertise that it is capable of all the formats, but they sensor is not really capable of it, and the camera does some internal interpolation to go between I and P. (apparently the Canon camcorders do this).
I can say that the 60i video out of my Sony camcorders looks gorgeous displayed through my PS3 to a 1080-60i TV. Better than any HD satellite channel. The image is very life-like, like you're really there. Great for home movies. I've read that anything intended for broadcast should be shot in 60i, but I'm not expert. I guess 120p would be the ultimate obviously.
But the interlaced videos are practically unwatchable on my computer. It's a few years old, AMD Athlon 64 x2 5000+ with an ATI Radeon 1600 PCI-E video card. The machine just chokes on it, it's juddery and full of combing.
Here's some testing I was doing on the weekend with deinterlacing. I was going to open another topic but, here you go.
http://www.vimeo.com/19897064
The left and center image are simply using the deinterlace techniques within Sony Vegas 10 Platinum. The one labeled "blur", I think adds the upper and lower frame of the interlaced video, and then adds a little blur to try and smooth it out. The one labelled interpolate, I think it throws out half the interlaced frames, and then interpolates the missing lines. The "blur" looks obviously blurry. The "interpolate has lots of jaggies. Look at the shut line of the hood on the Jeep. Overall however, the interpolate video is much clearer as you can see in the grass and leaves.
The "Yadif" on the right is a Yadif deinterlace technique. I used a freeware program called Handbrake to do it. Yadif uses and edge-directed interpolation algorithm to avoid jaggies. It's much clearer, everywhere, not just on the lines.
The video lost some quality, and picked up some judder when it went up on Vimeo. In fact, the discussion almost seems pointless after watching it on Vimeo as so much quality was lost anyway. The video runs smoothly on my computer, and the quality difference between the samples is even bigger. It's a hassle to run every video through Handbrake before cutting it up in Vegas.
So that's my rule of thumb. Internet vids should be 30p. Broadcast 60i. 24p if you are attempting cinema. Obviously if you could shoot 60p or even better, 120p, you'd have the most flexibility to downsample to whatever you want. Of course, shooting 1080 at 120p would take a staggering amount of memory.