The old mop and bucket.

Take a look at the eq settings in addictive drums 2 for the various kits.

Very careful gating (i.e., adjusting the parameters of the gate) followed by manually removing anything the gate did not catch.  Personally, I like the Sonitus gate.
 
Mic’ing inside of the bass drum helps.
 
For mic’s outside of the bass drum or even a mic on the underside of the snare a tunnel may be helpful.  This can range from a professional mic isolating setup to a simple moving blanket.  I’ve experimented with moving blankets and found them to be from modestly useful to a waste of time … but modestly useful might be all you need so, worth a try.
 
The crash cymbal bleed in the bass drum mic can be problematic when trying to get a cymbal crash to sit in the mix.  If you find yourself doing something like putting a volume envelope on a crash hit in the overheads you may want to listen for the amount of bleed in the bass drum.  A better option might be to simply cut and paste the bass drum happening under that crash.

Living Room Rocker
The old mop and bucket.

I love this place
 

quantumeffect
 
For mic’s outside of the bass drum or even a mic on the underside of the snare a tunnel may be helpful.  This can range from a professional mic isolating setup to a simple moving blanket.  I’ve experimented with moving blankets and found them to be from modestly useful to a waste of time … but modestly useful might be all you need so, worth a try.
 
 

Umm ... what is a snare tunnel and moving blanket...?

Here is the professional version of a tunnel (i.e., mic isolator) from Clearsonic.  You can do a homebrew variation using boxes or milk crates for structural support and then drape quilted blankets (or moving blankets) over the whole thing to isolate you mic.

http://www.clearsonic.com/skt3.htm
 
Isolating the bottom snare mic entails wrapping the snare like a skirt with a blanket.

Here is a fun article from Drum magazine entitled "How To Re-create Drum Sounds Of The 1970s":
 
http://www.drummagazine.com/plugged-in/post/gotta-have-that-thump1/
 
If you toggle to the 2nd page of the article and scroll down to figure 5 you will see a snare wrapped with a blanket/skirt in an effort to isolate the bottom mic.

Thanks quant, very interesting and creative.

I was a studio drummer for years in L.A. in the eighties.  Never used a blanket under the snare but it was common to drape a really heavy blanket over the kick and kick mic. Bleed was controlled through proper mic placement and EQ. The engineers were very good at checking for phasing between mics using a phase meter and listening in mono. 
I always used my wallet on top of my Ludwig Supraphonic 400 snare which muffled the ring.  I taped toilet paper to the toms with masking tape as close to the rim as I could. 
I used Remo Ambassador heads on the top and Diplomat clears on the bottom of all toms. 
Charles Ferris, Chief Engineer at Captial Records, would then roll off 15db (or so) of 400 hz from all drum mics. We did a lot of work together in Studio A and B there.
 

I can only speak of my experiences but they may lend some info.  I believe if you close mic well and set the gains correctly on the way in, the signal to noise ratio will be very high on the close mics. ie the sound they are intending to hear will be just at the right level and any other unwanted sounds will be at a very low level. And low enough to gate easily or use a downward expander set the right way.
 
I have found Rode NT5's are excellent as overheads, slightly out the front pointing in toward the kit and up at a reasonable height.  If set correctly these OHeads can actually reject a whole band and a PA even very well.
 
I play a Sonor kit and the drums are exceptional.  For kick I have got the hole in the front (6" or so and I put the mic right inside.  I have got a little blanket my son used to lay on as a baby, when folded up just right sits nice in the bottom and can be easily adjusted inside.  It just touches the front and batter heads.  I find this internal blanket can be used to really set the kick drum sound from well rounded and longish to short and snappy.  I sometimes place a small brick on the blanket once it is sounding right and it never moves after that.  Don't forget wooden beaters sound very different to felt beaters. Use the right one for the style in hand.
 
On toms I sometimes use those damping rings which you can buy or make from old heads.  I have made those hoops from 1/4" wide up to 1" wide for all head sizes.  The wider ones dampen the toms much more.  The narrower ones let a little ring back in and on the snare that can be real nice. It is easy to get a decent tom rock sound with those.  In other more Jazzy situations I tune the toms differently and let them ring more naturally of course.  Pitches need to come up for Jazzy styles and lower tunings for Rock.
 
Most of all get the drums sounding killer in real life then you will have an easy time thereafter.
 
On the hats I mic them with a condenser mic but have the rear end of the mic facing the snare and the front part aimed at where you are hitting the hats.  With care you can reject a lot of snare here.  Filtering after the recording in post can do wonders too on hat mics.
 
It is very essential to not only play nice groove wise but hit all the surfaces you have available with the correct amount of force to just make the sound you are after.  Cymbals do not need to smashed in order to hear them, often they only need to be stroked.  (tell that to EVERY drummer you know!)  The snare is a loud drum and too many drummers play it too loud.  Toms and the kick benefit from a bit of power behind those strokes.  Beater control on the kick is important too.  It needs to hit the head and get right out of the way of the head immediately after so the head is free to vibrate and hence complete the sound.
 

Rimshot
I was a studio drummer for years in L.A. in the eighties.  Never used a blanket under the snare but it was common to drape a really heavy blanket over the kick and kick mic. Bleed was controlled through proper mic placement and EQ. The engineers were very good at checking for phasing between mics using a phase meter and listening in mono. 
I always used my wallet on top of my Ludwig Supraphonic 400 snare which muffled the ring.  I taped toilet paper to the toms with masking tape as close to the rim as I could. 
I used Remo Ambassador heads on the top and Diplomat clears on the bottom of all toms. 
Charles Ferris, Chief Engineer at Captial Records, would then roll off 15db (or so) of 400 hz from all drum mics. We did a lot of work together in Studio A and B there.
 

Isn't it amazing that TODAY, we allow that ring we used to eliminate back then, Jimmy?! LOL!! Moon gels really do a nice job when you need a little control without totally making things dead. It's funny, I never thought I'd allow ring in my stuff because it just sounded over-bearing.
 
Then one day, after really listening to a recording I did for a client that used a really cool sounding Rogers kit, it dawned on me....."this drum sound sounds like when I play on the boxes in my warehouse when I do my day job shipping and receiving!" And they did. We used to tape, muffle and "wallet" everything to the point of deadness and things sounds like hitting a cardboard box. I'm SO glad I saw the light and allowed for some nice resonance and ring. Those little torque wrenches for drum tuning are quite good also. Though I like to rely on my ears, I've enjoyed the sound of near perfect tuning with the torque wrenches as they provide excellent tone and control of the bottom heads. (which in my day, we used to remove! LOL)
 
-Danny