Absolutely!
When I was about 12 I made myself a 'scope' from an old valve TV set. Sweep speed was either the TV line or vertical rate, and an op-amp on veroboard provided the single input drive to the other deflection coil. Can't recall if it was a 709 or the newfangled 741. Worked fine.
Of course triggering was a bit iffy (well non-existant really), and I don't think I could even spell caliba... calibrak... er, that at the time.
Did you know that a CRT electron beam could bore a hole in the glass, if you left it in one spot? It's these little details that separate the real EEs from the wannabees.
But seriously, on scopes, the answer is 'it depends what you really need'. Just a few comments:
* First starting out, why buy new when you can get great used test gear for very little cost on ebay and surplus shops?
* For old analog scopes, I love the Tek 7000 modular range of mainframes and plugins. So flexible, and the ergonomics of the controls is beautiful.
* The best thing about Tek & HP gear of that vintage, is you can get the full op & service manuals (including theory of operation and calibration proceedures) in either original paper (beautiful foldout schematics!) or on CD. Try getting full schematics for contemporary test gear - good luck!
Having a real service manual, and dirt cheap 'spares units' available means you can fix the things yourself, ie not for untenable costs from HP/Tek service centers. This goes for all sorts of test gear, not just scopes.
* Otoh, nothing old is going to be able to interface to PCs, for storing waveforms, etc.
Consequently, one also needs some newer digital scope. But still 2nd hand/ebay, etc.
Doesn't hurt to have several scopes anyway. Especially when you need to fix one scope.
I've a simple old Trio 100MHz and a HP 54121T 50GHz DSO/TDR on my workbench, one Tek 7000 series rackmounted scope in each of several equipment racks, a Tek 465 on a trolley, and an assortment of others shelved.
* One thing about LCD screen DSOs, I don't think anyone else here has mentioned. Beware the EMI from the LCD backlight inverter and fluro tube. This really surprised me when I discovered it with a Tek DSO at work. Can't recall what model it was, but was brand new around 2004-ish. Working on a circuit with millivolt signals, noticed an excessive amount of noise being picked up from somewhere. Turned out the scope itself was radiating! Holding a bare probe tip near the edge of the screen or plastic case nearby, was worse than the flyback EMI from a glass CRT - but at the backlight inverter frequency. Note to self - never use a backlit LCD scope with a plastic case.