I am depressed by the unspoken assumptions in this question and in all the responses (save Erik's -- Dios Mio!) so far.
There is a presumption in the minds of digital recording engineers that "tape" or worse yet, "the analog" has "a sound," and that that specific sound can be had somehow, other than by recording on tape.
Hooey.
The underlying presumption that this sound can be imagined and then modeled and then applied is so completely baseless that we are now on the fourth (tenth?) generation of simulation devices and software, as if the persistent attempts and failures weren't enough to demonstrate the chimerical absurdity of the task.
I have been using tape machines of all stripes every damn day for several decades now, and I'd like to think that I listen carefully and pay attention, but try as I might, I cannot come up with a specific set of artifacts that I can attribute to tape alone. Every tape machine sounds different. Every playback chain sounds different. Every use or abuse of tape sounds different. Sometimes every damn snare drum hit sounds different.
Take something as "simple" as tape "compression" (saturation), a touchstone of the "we can simulate it" crowd. I never operate tape machines in saturation, and having done extensive experiments, have concluded that it almost always sounds "like shit." Of the things I like about analog tape, I like most that what I record on it comes back sounding pretty much like the source.
I would argue that the majority of all great records recorded in the analog era were recorded by trained, careful engineers who would also avoid saturation, yet "tape compression" is often cited by the inexperienced as a reason those records sound good, not the more complicated, less encouraging truth: That everyone involved was good at his job, and there was no magic -- no "secret."
I consider the search for synthetic "tape compression" to be an attempt to emulate a failure mode, and an unworthy effort, albeit one with a lot of gullible clients.
Properly-working analog tape machines are not magic boxes that make bad sounds good. I know, because I've been able to record a lot of bad sounds. They are also complex systems, with many interwoven design and practical compromises, all of which will affect the recorded (or played-back) sound. There is simply nothing that can be derived (in such a way that you could put a knob on a device and have less or more of "the sound") that will do it.
Not only is there no single "sound" to shoot for, the number of variables involved makes simulating the system itself a rat's nest of individual problems to solve, even if there were a target to shoot at.
Tape stock, head gap, head wear, bias level and frequency, bias depth, HF headroom / self-bias, print-through and absolute level are all interacting variables, as are the topology of the input and output electronics, damping from upstream- or downstream sources and loads on those electronics, record EQ emphasis, out-of-band partials...
I'm not suggesting that tape is magic -- far from it. I'm saying that analog systems are different from digital ones, and you shouldn't attribute to one or the other a magical quality that will get you out of the weeds. Use real, definable effects to describe your perceived sound and then work from a basis of problem solving.
If what you want is compression, then by all means use compression. If what you want is distortion, then by all means... You get the idea. If you want to try one of these combination distortion/compression boxes that purports to have "the analog sound," be my guest, but you shouldn't carry on with the delusion that what you're getting is based on the sound of tape.
Analog systems have noise and distortion, sure. Small, generally insignificant amounts of both. Operated like a baboon, you can even saturate or distort them. These specific, individual defects can be simulated, but they are not why analog tape is used. Reliable, good sound and permanence are why, among other more involved reasons.
Let's say you see a real fast car, and notice that it has dents in its fender. You go home and dent your Rambler, thinking that will make it go faster, and are disappointed. I suggest that the attempts at simulating "tape sound" have it exactly that wrong.
