So, I recorded a new jazz Christmas jazz tune for my church's upcoming CD- it's a small trombone jazz combo. I'm wondering what kinda sound I can get if I were to run the recording through a cassette player, for example, then maybe compress that and put it beneath the master or something?
What sorts of different sounds have you guys been able to get with a cassette deck (in the digital realm)?

I haven't tried the trick of re-recording through a cassette, but I did mix down to cassettes for many years so I have a pretty good idea of what that would sound like.
 
Severe tape limiting can do a lot of the mastering work for you. When I was bouncing mixes to cassette I never used a limiter - the tape does that for you. Of course, I was also coming off of tape, so that helped too. Coming out of the computer I'd use a limiter as a safety mechanism and be cautious of sending too hot a signal. A little tape distortion goes a long way. Also be sure to use a deck that either has no AGC circuit or has one that can be bypassed.
 
For brass I'd be inclined to boost treble on the way in, so you don't lose as much off the top and you can mitigate tape hiss a little. 
 
Go for it! 

Parallel cassette compression.   You never know until you try although I"m skeptical.

In the late 70's, I used to run my 8 track mixes through a getto blaster and took the line out to my 2 track. 
It had a super fast stereo compressor built-in and really made a hard hitting master. 
I controlled the input level from the 8 track mixer. 
 
We got a record deal with those masters.
 
For the Op, this is a different technique than running through a cassette player and I don't think they make the kind of quality getto blaster available 35 years ago but just wanted to chime in here. That brought back some good memories.

You might want to be careful especially with timing.  If you have a great stereo mix coming out of your DAW and you decide to record that onto a cassette then you might want to be aware of the limitations of the cassette medium in terms of speed accuracy etc.  It wont be in the same class as digital is.
 
So if you intend to import the cassette recording you might have to line it up rather carefully under your DAW stereo mix to ensure the two line up OK.
 
Then you could try adding some of the cassette sound in under your mix. I would not be replacing your DAW mix entirely however with the cassette mix.
 
There are some great plugins out there that can do very similar stuff. eg great tape saturators or Klanghelm's SDRR plugin. Or a combination of both.
 
http://klanghelm.com/SDRR.php
 

I'm not sure why you would do this...as Jeff says use a tape sim...my master buss consists of sonars tape sim first and after I've compressed and EQ Kramers Master tape.
 
Ben

There was also that one effect from the KVR challenge which had a microcassette simulator as one of the options.

This topic comes up once a week on GS forum. The answers are always the same. 
Why? It is usually the beleif of the thread starter that analog is better ( a whole debate in it self)  and a cassette is the only analog recorder they have on hand. 
First- Any analog tape decks still around are ussually in pour shape. Even the Cassettes themselves are no longer produced and quailty is not the same as it was in the 70's and 80's. 
Second- the exact same results can always be had ITB if you know what your doing.