Can you get great analog sound from analog tape?

Can you get a great sound stage with analog tape such as a good quality reel to reel or cassette. If you record from a good quality turntable to tape will it be nearly as good?
Schange, reel to reel, to both of your questions the answer is yes, IF you use a top deck and as I learnt, good cabling, both ics and pcs and power conditioning. As to casettes, in my opinion, the answer to both questions is a resounding NO!
There is an excellent RtoR machine that you can get used which is OTARI MX5050 B2. This machine is being or used to be used as a broadcast reproducer. To tell you for sure that Carnegie Hall in NY is still using it for live recordings. Among Reel to Reel machines there is none that I've ever known for the better 2ch performance.
Analog tape running at 15 or 30 ips with Quantegy 499 or GP-9 tape is superior to just about any recording format out there. The biggest issue with running analog tape is the cost ($20 for ~30 minutes of 1/4" tape at 15 ips) and maintenance (cleaning the machine after each use, demagnetizing, making sure that the tape is properly packed on the reels). Properly maintained open reel tape is not a user friendly format. Running the tape at slower speeds with less expensive tape or recording onto a consumer quarter track machine will yield decent results but you are better off with a good CD-R at that point. Keep in mind, to achieve proper performance the bulk of the cost is in the tape, not in the machine.

The Otari 5050 mentioned above is a great machine for not a lot of money these days. They can be had on the used market for < $1,000. However, if you are looking to spend a little more (approx $2k), you can get a Studer A-80 which is both sonically and mechanically better than the 5050 but takes up a lot more room. The nice thing about the 5050 is that it gives you a lot of bang for the buck. The step up from that is the Ampex ATR (especially ones modified with the transformerless I/O boards) or a Nagra. However, these machines will cost upwards of $5-6k for a 1/4" machine.
Soundstage? Sure. Speaker/room interaction (along with the original recording) is the key factor in soundstage, so the key question is, how well does the recorder preserve the locational information on the original recording? Good reel-to-reel certainly will. Cassette's a bit dicier, since you certainly lose something with the inevitable dynamic compression.

If you're thinking more generally about "that vinyl sound," yes, a good recorder will capture that--just as it captures all the pops and clicks. :)
Analog 1/4 inch reel to reel is a superior format to both red book CD and vinyl records. An even better format is 1/2 inch reel to reel. Unfortunately, I agree with the above that it's expensive, maintenance intensive and not particularly convenient.
I get great sound daily from analog tape, playing back anything from production master dubs to factory pre-recorded reels. There are various factors that determine sonics with reel tape, such as: head gap, head quality, tape speed (of course), electronics mods (such as mentioned previously, by-passing coupling transformers, etc.), tape quality, mechanical modifications, and even the quality of the recording. Now some of the drawbacks: 1)Back coated reels require occasional "baking" in special ovens which cost $400 to $500 new, though I found one for $275 used. 2) Real production master dubs are quite expensive, as you can imagine, and are nearly impossible to find. 3) you have to play through an entire reel to hear the last song, otherwise you risk stretching the tape. 4) Good heads are expensive, great ones are worse. The best Saki heads run around $1500. 5) it takes several minutes to reel the tape onto the machine, prior to play. 6) Many of the Ampex ATR models are mechanical nightmares, and require constant maintenance. (I have 2 for sale now, want one?). I'm not trying to discourage anyone, just inform them of what they will experience, as I have already. Is all of this worth it? Hell yes!
cassette decks don't cut it?

I make some pretty nice tapes with my Nakamichi 3 head deck
Granted reel to reel can be better but you would be surprised at the results of a good cassette deck and the taps are very cheap these days ($1.25 per tape at sams for Maxell XLII). I play cassettes in the car, don't want to deal with a cheap car cd player or ruining my disks

I would love to have a 4 or 8 track reel to reel to record my own music tracks, but the players I've seen are pricey, and you can get an 8 track BOSS digital setup for $500
I must agree with the posts above. One caveat: tapes are expensive and not always easy to find. BUT, recording from vinyl with care (i.e. paying attention to wires of all sorts as Detlof notes) you would need a VERY revealing system to gauge sonic differences -- esp. if you're well calibrated &, I've heard (i.e. hadn't tried), if you use dolby.
Since I don't own a reel-to-reel, I cannot attest to this, but I'd be a bit surprised if an analogue tape copy were truly sonically indistinguishable from the vinyl original. Whatever wires you used.
I use a Nakamichi CR-7A, which is calibrated and clean. It makes very acceptable analog recordings. The noise floor is higher, but the imaging is right on with the source. I use this primarily to tape things I either wish to keep stone mint or can not obtain. I also have a Sony ES DAT deck, but I find myself using the Nak more often even with the DAT run through an Ultra Link II DAC. Tom
Bomarc: you're right in yr post above (doubting that tape is indistinguishable fm vinyl). I should have noted "subjectively" indistinguishable!
I find that the musical "essence" is retained i.e. the intrinsic qualities of vinyl are easily perceptible. In my experience, the tape (used to) draw me into the music more than into the reproduction quality of the medium (the latter happening to me when I listen to the cd version of a vinyl I have).
Agreed, Greg. A good tape recording of vinyl playback will certainly capture the "intrinsic qualities of vinyl," as you call them. Whereas a CD made from an analogue master tape will not. (Which just goes to show that it's not being analogue that does it; it's being on vinyl.)
I somehow doubt ( though cannot prove ) that it is vinyl, which "does it". To my mind and experience it is rather the analog process. Classical music on an ADD CD sounds generally better than a DDD redbook CD. But the limitations inherent in the redbook processing, does not seem to capture all of what is on an analogue mastertape even through an ADD CD, even with upsampling, if you compare it to a LP or even a good commercial tape of the same original recording. At least, that has been my experience so far.