More than one text that I have read so far has said this. Digital scopes are good for making automatic measurements. Analog scopes are good for seeing waveforms accurately and seeing quickly changing information. You don't get both with any instrument. Is this still true? If the analog scope is still a required instrument, why are there no large manufacturers selling them? It seems there may be some ones out there, I still see analog scopes at Fry's (similar to http://www.jameco.com/webapp/wcs/stores/servlet/Product_10001_10001_1536886_-1) but I always have the feeling these may be new old stock or smaller manufacturers still doing small runs when there are parts for them. Is anyone even still making CRTs necessary for these scopes anywhere in the world?
I don't know if it is mandatory/good/bad/whatever... but I personally have both.
I suspect it's more a matter of one's personal experiance and what they learned with when first learning electronics. The modern digital scopes offer many features and functions that a analog scope just cannot do, but I feel very comfortable about what I can and cannot do with my trusty Tektronix 2213 analog scope and plan on having it buried with me when I pass. 
Lefty
A good storage 'scope will catch events you'd not be able to see on an analog 'scope - no amount of upping the brightness will persist a 50ns event for long enough to be see by the human eye.
Having said that there are storage scopes using a storage tube that do solve that problem without an ADC: History of the oscilloscope - Wikipedia - find a secondhand one?!
I've just moved from analog to digital scope - old analog one I built from a kit / electronics magazine design a long long time ago, too slow really. New digital scope is nice by comparison 
I have a Tektronix 2236 for a couple of months now and I must say I haven't used it that much. But it is good to have around when it's needed. If you can find one cheap, I would definitely get Tektronix or a quality unit.
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 “infinite” resolution. That’s nonsense, since the noise floor makes the resolution/accuracy far worse than a CD. It’s OK to prefer analog sound if that’s what you like, but digital is technically superior. Or, it’s like saying that my “analog” ruler is better than my digital calipers.
One “interesting” thing is that the screen resolution on my Tektronix ‘scope is “only” 8-bits. That seems terrible, but that’s 256 “dots” which is about half that of DVD. I'm pretty sure you can't see a 1-bit change on a 4-inch screen.
I have both, neither one very serious, but they are extremely handy. I use the scope way more than the LA, and the only time it really comes out is when I need to debug a stream of data.
You don't get both with any instrument.
You can, my scope is a Kenwood DSO from 1987, its only 20Mhz, but its a CRT based machine with both analog and digital storage functionality, and its very rare that I switch it over into analog mode. Last time I did I was looking at a 28.something Mhz crystal and the DSO couldnt latch onto the very short peeks 8Mhz past its bandwidth (but the analog function showed it).
Fully digital seems to be king, cause its cheap, and today its pretty damn fast, there is always a hint of lag, but there is so much memory available and features in modern models, it more than makes up for it.
You cannot be a serious EE if you have to have both digital / analog scopes.
humbug, even in our LAB at work, sitting next to the tens of thousands of dollars Tektronix with its dual LCD's we keep the old analog only scope around ...why?
its for when the noobie starts getting mouthy so we can threaten him with it
You cannot be a serious EE if you have to have both digital / analog scopes.
More rubbish from dear Henry.
There are expensive digital scopes with digital phosphors but they don't work in all situations.
The main use of an analogue scope is looking at a modulated signal on a HF carrier, try that on even the best digital scoopes.
A couple of years back I managed to snag a nice Fluke Combiscope; it's an old dual-channel DSO with both analog and digital modes (you can set the traces so that one is analog, one digital, or both analog or both digital). You'll only find such a scope, I believe, in those with real CRTs. They likely don't make them any longer.
I'd say ultimately the answer would depend on what you plan to do in electronics. For most hobbyist needs, a cheap 50 or 100 MHz Rigol or similar DSO would be all that would be necessary. The only time you might find yourself needing an analog scope would be for things where you need to catch the "transients" that the sampler might miss (as has been pointed out by GM above).
If you know what you are doing to test out a scope, and can do it in person, buying a used analog scope can be worth it. I picked up a Tek 2213 on craigslist this way (it had even been factory calibrated). The only "repair" I had to do to it was replace the implosion shield (the old one had gotten fogged up - I knew this when I bought it - the replacement came from this Tek parts site in Czechoslovakia). I paid $250.00 for it (the Fluke I only paid $200.00).
One thing I did find out real quick was that even on the used market, once you advance beyond 2 channels or 100 MHz of bandwidth, the prices skyrocket like nobody's business (though I did once see a nice Tek 4 channel scope at a local ham fest for about $250.00 - so it is possible to score them occasionally).
If you work a lot in the digital domain, a logic analyzer or a protocol analyzer would be very helpful as well.
dhenry:
If you work a lot in the digital domain, a logic analyzer or a protocol analyzer would be very helpful as well.
Got one, one of the cheap 8 channel Saleae units. It has helped me several times and is just fun to see how the Arduino is actually banging out the bits.