TIRES

Ever wondered what kind of tires to buy for your Mountainbike? Here IS info to help you decide on a first-rate tire for your next ride! Now get out there and wear out that rubber...

KNOBBLY

This is one of the most fashionable tire designs for aggressive mtber's. They dig well into loose soil and mud, and give outstanding grip. Sometimes they are explicitly designed for the front or the rear tire. The tread pattern on the front may be for better rolling resistance and for firmly holding in turns. The rear is designed more for traction when accelerating and grip when climbing.
Widely spaced knobblies have less traction on smooth surfaces but limit mud accumulation. Closer spaced knobblies are best in firm and dry conditions and reduce rolling resistance.
These tires do pretty well over logs and they are also superb in mud. On dry smooth surfaces, get the smaller, closely spaced knobs. Usually also comes in FAT tire sizes.

Other factors- A set of knobblies may weigh a little more.
They may have poor traction on wet pavement.
Also, they will have more rolling resistance than a smooth tire design.
Avoid use on smooth rock surfaces like river rocks. 

HYBRID

A hybrid tire has the tread cut into the tire (sort of like your car), rather than protruding like the knobs. This is a great tire for riding on roads, hard pack, or smooth surfaces. This design has good traction on the forest floor or hiking trails that are relatively smooth.
They offer less rolling resistance than a knobbly, and are quieter on pavement.
Hybrid bikes usually come with this tire design.
A "Trials Universal" design is a cross between a hybrid and a knobbly. It usually has a uniform checkerboard pattern tread and can be used as a hybrid or a knobbly. It is a good all around tire if you occasionally ride the jeep roads or hard surfaces.

Other Factors - Most bikes come with Hybrid tires from the bike shops.
Like knobblies, there are many different tread patterns.
This is a good tire for beginner or intermediate mtb'er.
Usually need directional design for the front tire, which may have different tread design than the rear.

SLICKS 

These tires have no tread to speak of. They are totally smoothed similar to a road bike tire. Made to be ridden on pavement, many riders use these on smooth rock like river rocks. They have very little rolling resistance, and can take a high air pressure. Usually they are only 1 to 1.5 inches wide and are supposed to be rare on a mountain bike, but looks to me there are still a lot of fearful mtb'ers who do road races on slicks. Come on leave the tar... get some dirt action!!

Other Factors - Slicks may be O.K. on super hard dirt and are fast tires.
You can go close to or over 100 psi. in most slicks.
They are dangerous on wet pavement.

SEMI-SLICKS

Semi slicks have knobs along the edge of the tire for good grip in the turns, but have smaller tread in the centre. This allows a faster rolling tire. You will not have as good of traction when climbing, and it may perform poorly in wet slippery conditions.

Other Factors - This is a highly specialized tire for use in specific conditions. Not a good all around choice.
Can be useful on certain tracks where speed on the straights and traction in cornering is needed.

 FAT TIRES

This refers to a tire that is wider than most tires, say 2.25 and over. Usually a knobbly design, sometimes a hybrid, these tires are for downhill, mud, loose surfaces, and wet conditions and overall use. Some mtb FAT tires go up to 2.75 or 2.9 in width. ~Caution~ any wide tire has to have room to fit on your bike. It must not rub the chain stays, front derailleur, or brake housing.
Some riders like to ride fatter tires in the front than the rear. I prefer fatter in the rear than the front.
They weigh more than narrower tires, and have more rolling resistance.

Other Factors - These tires may offer good traction when climbing, but because of their weight it may be harder to pedal uphill.
It may be noticeably harder when staring the bike from a stop, as these tires require more effort to get rolling.
Their extra weight can give your more momentum when going downhill, and offer more floatation over boulders, bumps, and rough surfaces.
On a rigid frame bike with no suspension, a fat tire can provide some degree of suspension as they usually have a higher profile and can be run at a lower air pressure. 

Almost all mtb tires come in 26" rim size. Make sure you have the proper width tube, usually 1.5, 1.75, 1.95, 2.125, and 2.25. Check the tread pattern, see if it is front or back specific, and see if it is directional (look for arrows on the tire sidewall). Make sure it will fit on your bike if it is FAT. Ride the proper pressure, and always carry a patch kit and pump. Buy a brand name and don't economize here, this is an important part of your bike!