N particles, will there be any rotation after a period of time or everything will collapse This is in context of classical Newtonian physics.
Consider a system of n different point mass particles. Initially all are spread around on one plane. No particle possess any velocity to begin with. There is no external force acting on this system. Each particle has some mass. The only force to consider here is gravitation between any two particles. 
When two particles collide, lets say they form a lump with mass equal to sum of the two. This now behaves like one single particle.
My first assumption is, the centre of mass of this system, throughout time won't move. Right?
Given a sufficient amount of time, will everything collapse into one single particle at the centre of mass? 
Or it's possible to see a system where few particles are rotating in one direction and other in other direction, so that angular momentum is conserved and net angular momentum is still zero? 
If yes, can you give one simple example with points, mass and initial position which will achieve this kind of state.
EDIT: On similar note, can we have say 3 particles which are attracted to each other but never collide, something like a simple harmonic motion?
 A: Well, the planetary system is an example, though it is not isolated as in your problem.
What you are requesting is a simple solution to a many body problem. It does not exist.  Deterministic chaos is one way to study such problems, also numerical solutions in computers.
For example here is such a study:

Onset of Secular Chaos in Planetary Systems: Period Doubling & Strange Attractors

Also here , from their abstract:

Over the last two decades, there has come about a recognition that chaotic dynamics is pervasive in the solar system. We now understand that the orbits of small members of the solar system—asteroids, comets, and interplanetary dust—are chaotic and undergo large changes on geological time scales. Are the major planets' orbits also chaotic? The answer is not straightforward, and the subtleties have prompted new questions

Numerical solutions are used in the virtual planetaria.
So as genneth has said angular momentum and momentum will be conserved, but that is the only sure statement for an N-body gravitational system as the one you postulate. (same is true in N body systems for other forces too). Since you posit initial conditions at rest the total system will have 0 momentum and angular momentum, but some individual orbits will appear as not all solutions will be head on collisions. Rather the opposite, unless there is one very large mass particle to start with at the centre of mass.
A: If you are thinking about largeish N (hundreds to millions or more), then it resembles a star cluster. There is the issue raised by more than one other poster, that if they are point particles, they can't combine/stick. Close graviational interactions resemble a sort of collision. Some particles will leave collisions with enough kinetic energy to escape from the system (i.e. fly away, and maintain a nonzero velocity in the limit where time goes to infinity), so you get a clump of gravitationally bound particles, and occasionally a particle acquires enough kinetic energy to escape from the collective graviational embrace.
In a truly 2D universe, the configuation will stay 2D, but in any real 3D situation any infinitessimal motion in the third dimension will cause the system to spreadout over three dimensions. I believe it reaches a longterm quasi-steady state that resembles a globular cluster, but remember that occasionally a particle will escape, removing energy (and energy per mass) from the cluster. Also the net momementum and angular momentum of the bound particles, equals zero, but nothing constrains these two subsets individually to have zero momentum or angular momentum, so the cluster might end up with nontrivial momentum and angular momentum.
A: 
My first assumption is, the centre of mass of this system, throughout
  time won't move. Right?

Yes, by conservation of linear momentum.

Or it's possible to see a system where few particles are rotating in
  one direction and other in other direction, so that angular momentum
  is conserved and net angular momentum is still zero?

Even with only three bodies, solutions can be found where they escape to infinity (with respect to the center of mass). This requires a binary system to be formed by energy conservation. See figure 10.b at page 10 of this paper for an example.

EDIT: On similar note, can we have say 3 particles which are attracted
  to each other but never collide, something like a simple harmonic
  motion?

This is also possible. See "Periodic Solution Standish" at page 6 of the same paper.
A: It sounds like you've got a bunch of particles with $1/r^2$ attractive forces which (perfectly) inelastically collide. If so, the momentum and angular momentum of the system will be conserved, so the centre of mass will not move, and there will be no net rotation. A single "clump" in the middle is certainly a stable situation, and I think there cannot be others --- they will necessarily have finite angular momentum, though a proof escapes me.
