Does friction always oppose motion? Recently I had the following misconceptions: 


*

*Static friction always opposes the motion of body.

*The force of friction cannot initiate motion in a body.
Now I came to know that my understanding was wrong and that friction indeed can cause motion in bodies, and that static friction does not always oppose the motion of a body.
But I found this quite bizarre, how can a force which has always been taught to us to oppose motion, oppose points 1. and 2.?
 A: The top answer given is correct, but I wanted to slightly extend this:

how can a force which has always been taught to us to oppose motion, oppose points 1) and 2)?

Imagine a table, I slide a very heavy hockey puck over the table. Without friction, the puck keeps sliding. But because there is friction, the puck is slowed down.
Now let's put the table on wheels and do the same test again. Without friction, the table does not move and the puck slides right off. BUT with friction, the friction takes the kinetic energy of the puck and imparts it to the table. Because of this (and because we put the table on wheels), the table now starts moving forward.
Because there is friction, the kinetic energy is transferred from the puck to the table, which can cause the table to start moving (given the right circumstances whereby the energy imparted to the table overcomes the table's own friction with whatever it's resting on).

There are common real world examples here, e.g. someone who takes a running jump, and lands on a stationary carpet/skateboard, which then starts moving because the friction keeps the carpet/skateboard and the person's feet together and therefore the person's kinetic energy is (partially) transferred to the carpet/skateboard.
A: Friction opposes relative motion between two bodies. 
Note that might mean that friction can create motion relative to i.e. you. For example, dropping an item on a moving belt. Friction opposes and reduces the relative motion of the item and belt until they move together. But now they’ve started moving relative to you. 
A: The answer given by all others are much more better than mine, but here is my answer (essentially a rephrasing of the answer by @yuvraj singh)
Friction opposes the relative motion. For example, let us suppose that you have a car. Why does the car move forward, even if mechanical work is carried out only on the wheel? What is the missing piece here?

Friction

When you observe the lowest point of the wheel which is touching the ground, you will find it moving in the backward direction. Since friction opposes any relative motion, it would act on the wheel in the forward direction. This action of friction would impede the tendency of the wheel to move in the backwards direction. But, as a side effect, it would also push the car forward since the wheel is a part of the car.
A: Friction opposes the motion between THE TWO SURFACES IN CONTACT (the motion that would have happened if there was no friction). You can walk because the friction pushes the sole of your shoe forward. If there was no friction, the sole of the shoe would move backward (the direction you are kicking the Earth).
Whether those surfaces are in moving/rotating parts of a composite object is another story. Again, it is not about the relative motion of the bodies, but about the motion of the surfaces in contact. When the tires in your car are rotating, the point of contact of the tires against the road is pushing the road towards the back of the car. Without friction, the tires would spin in the same place. Because of friction, the tires push the road backward and, by the 3rd law, the road pushes the tires forward. That happens when you are speeding up. When you are slowing down, the point of contact of the tires with the road begin to push the road forward. Note that the car is still moving forward. That proves it is not about the relative motion of the bodies but about the motion of the surfaces (that would have happened if there was no friction). Ergo, the other answer is incorrect.

This is very interesting. The moderators erased some of my comments where my rudeness was on full display. Since my comments were correct from the science point of view (maybe not politically correct), I am going to double down.
One of my finest moments was on my reply to "Friction between a moving car and the road will only ever slow down the car (relative to the road), it will never increase their relative velocity." I suggested that if the author of such blasphemy truly believed that being true, then he/she/it should drive to the middle of a frozen lake, change the tires for some worn out ones, maybe douse some water around the tires to make the ice smother, and try to drive out of the lake. All hail darwinism. The exchange might have harmed some sensibilities, but the message was clear and correct. I hope he/she/it learned some Physics as Dude156 did on another of my answers. 
There was another fine comment mentioning that the most voted answer could be savaged by subdividing the bodies into the parts that are in contact and the rest of body. In particular, that post mentioned that tires have a so-called contact patch. Thus, friction opposes the relative motion of the contact patch of the tire and the road. I replied that such a point of view is less optimal than mentioning that friction opposes the motion between the surfaces from the very beginning.
See you at physicsoverflow. Peace out. 
A: Friction generally spoken causes a change in speed. Physicists call this change — in mathematical terms the speed's derivation — acceleration. While in casual language "to accelerate" means "speeding up", when physicists talk about acceleration they just mean speed change, in any direction.  
The underlying reason is that a body's initial speed, including its direction,  depends on the observer's viewpoint. The same force therefore can be seen slowing a body down or speeding it up.
Let's take as an example a bullet shot westward along the equatorial line1, with a nozzle velocity of about 465 m/s. The  bullet impacts a clay wall which it penetrates for a few centimeters before it gets stuck.
An observer on the grond has no doubt that the friction between clay and bullet slows it down until it reaches standstill. But on the equator the ground is actually moving with about 465 m/s, not quite coincidentally exactly the speed of the bullet: An observer standing "still" above the rotating earth would see the bullet stand still in space until it gets whisked away eastward by the rotating wall. 
The important takeaway is that how strong the wall must be to block the bullet, how far the bullet will penetrate, how much it will deform in the process etc. is entirely independent of the reference frame we choose. The same is true for the strength needed for rocket engines to lift a rocket off the ground in Cape Canaveral, the forces on a seatbelt when the car impacts a concrete wall at 65 mph, and all other physical processes. Nothing about them changes when we change the frame of reference, they all are equally valid.2
Bottom line: The same acceleration of the bullet by the wall can be regarded a slowing down  or a speeding up or any combination of the two, entirely depending on the observer's reference system. This indicates that the absolute speeds — on which it depends whether friction slows something down or speeds something up — are arbitrary assignments; only the relative speeds matter.

1For the short time we watch the process it is not a big error to ignore that no point on earth's surface is an inertial system (since the earth is rotating), and to ignore that the earth moves around the sun.
2The rotation of the Earth can actually not be neglected when launching rockets (time and distance exceed the small amounts during which it wouldn't matter) but the thrust needed to start depends on it only marginally. Similarly, if we consider significant fractions of lightspeed and significant fractions of the size of the known universe we cannot consider them all equal in cosmological terms: For any given point in spacetime there is a "most natural" frame of reference for which the universe appears the same in all directions, or is isotropic, the comoving frame, but that is beyond the scope of the question.
