I've read threads both here and abroad where "old school" guys will tell you to use some type of muffling on your drum heads. Maybe back in the 60s-80s, yeah.
I've also read threads where people don't use any muffling, and they go on to make a youtube video and their drums sound like utter crap, ringing WAY too much and for too long.
So which is it? Muffling or no muffling? That depends on your drums and your choice of drumheads. A good quality drumhead will have a self dampening ring built into it, which cuts down on the overtones, but they also prevent the "dead head" sound of too much muffling. If tuned properly, the heads will sound awesome, both naturally and with a mic.
A good quality drumset also helps. The type of wood (or plastic, metal) used WILL effect the sound you get from your drums. Cheap drums with good heads can sound decent. Expensive drums with crappy heads may sound decent for a while, until the heads give out. If you have expensive drums, buy expensive heads. You wouldn't put cheap gas in your Ferrari, would you?
My personal preference for drumheads on my TAMA set are Evans G2 batters, EC2 RD for the snare, and Remo Powerstroke 3 for the basses. I feel these provide the best amount of self muffling while maintaining the musicality of the drums. Yes I have a normal sized pillow in each bass as well. This gives them just enough resonance to sound really good, with a deep thump and a hint of sustain.
As for tuning, I use 2 different things: by ear, and a TAMA TW100 tension watch. I start by seating the drumhead on the drum itself, putting the rim on it, and finger tightening each lug down. At this point I press down with my fist in the center of the drumhead to make sure it "seats" properly. You will hear a little popping going on...that is normal. Then I take a drumkey and give each lug a full turn to remove all wrinkles. Make sure that when you are tightening the lugs that you work across the head, i.e. tune the 12 o'clock position, then the 6 o'clock, 3 o'clock, then the 9 o'clock.
I tap around each lug, appx. 1" from the edge and try to find a sound that I like. Once that sound is discovered, I make sure the other lugs are producing the same sound. This may call for some extra tuning of the other lugs (up or down)...so be it.
In comes the TW100 tension watch. I place it 1" from the rim by each lug and check to see what the tension is on that lug. If it is on the lug that I want my preferred sound to be based off of, I'll record that tension and then make sure the other lugs are as close to that number as possible. Be prepared to go back and forth with the other lugs until your ear tells you "this is the sound I want!" This makes the sound uniform throughout the drumhead.
The great thing about this is that once you achieve the sound you want, with just the right amount of resonance, you can record the tension numbers down for ALL your drums and come back to them when you replace heads for the exact same sound.
It is also worth noting that I tune the resonance (bottom) heads first, then the batter (top) heads. The bottoms will be slightly lower than the top. If you already have both heads on the drum, make sure to muffle the one not being tuned by placing it on a pillow, in order to kill its resonance so you are focused only on the head you are trying to tune.
I have found that my rack toms are usually in the 55-60 tension range on batter heads, floor toms are in the 50-55 range, my basses are right at 50, and my snare is cranked way the hell up for an ear piercing CRACK, with a tension reading around 80-85.
Whether I am in my den, on a stage with no mics, or completely mic'd up, this type of tuning sounds AWESOME for rock/metal. If you use a lot of muffling, your drums will sound dead, and if in concert the crowd can't really hear what you're doing over the screaming guitars, bass, keyboard, and vocals. My opinion is to do away with muffling (except basses), get good heads with built-in muffling rings, learn to PROPERLY tune your drums, and be confident that you have a good sound.
If you find that you still have too much resonance, you can always put a piece of Moongel on your drumhead and it will take out some of the ringing. Look it up for more details about its use.
There is a reason why drumhead manufacturers are now making their "top of the line" heads with built-in dampening rings. If you know what you're doing, these eliminate having strips of felt from hanging off your toms, napkins taped to heads, or some other "old school" trick for tuning your drumset. Technology advances...so should tuning techniques.