I don't own a 'scope, but sometimes I lust for one! 
I've rarely needed one (for analog or digital stuff), and since I work in electronics I can bring my hobby projects into work on the weekend.
We don't have any analog 'scopes at work anymore. As far as I know, there is no advantage to an analog 'scope as long as they both have the same speed (MHz). The Tektronix digital 'scope on my bench right now is rated at 100MHz, with a sample rate of 1.25GS/s.
Analog waveforms look perfectly "smooth and analog". The measurement features are a nice bonus... It measures period/time, frequency, and voltage (and maybe some other stuff I don't use). Another nice thing with a digital scope is that you get a "nice picture" no matter what you are looking at. For example, when you look at a very low-frequency waveform (let's say 1Hz) on an analog 'scope you don't get a waveform, you see a dot tracing across the screen. If the frequency is a little higher, you'll get a waveform, but it will flicker. Or, if you're looking at a short pulse with a low repetition rate, it can be very-dim. On the digital 'scope you can always see the pulse, and I never even touch the brightness control.
It might be like the analog audio myths⌠A lot of audiophiles seem to think that analog vinyl has âinfiniteâ resolution. Thatâs nonsense, since the noise floor makes the resolution/accuracy far worse than a CD. Itâs OK to prefer analog sound if thatâs what you like, but digital is technically superior. Or, itâs like saying that my âanalogâ ruler is better than my digital calipers.
One âinterestingâ thing is that the screen resolution on my Tektronix âscope is âonlyâ 8-bits. That seems terrible, but thatâs 256 âdotsâ which is about half that of DVD. I'm pretty sure you can't see a 1-bit change on a 4-inch screen.