Will overlapping two different beams of coherent light cause interference? I have two laser beams with same polarization running parallel to each other. Will they interfere? If yes, then what are the conditions (perpendicular distance etc) and how can I observe the interference pattern?  
 A: I'll assume that both lasers are of the same type, i.e that both are generated from the same physical mechanism.  All lasers have some tuning range over which their wavelengths can vary.  So, even though both are very monochromatic (single frequency) they will, in general, not have the exact same frequency.  A HeNe laser, for example, has a tuning range of $1\ \text{pm}$ or $\sim1\ \text{GHz}$.  Which frequency actually lases depends on many things, but it can be tuned by changing the temperature of the laser or by adjusting the resonator length inside of the cavity.  
So, what happens when you overlap two different lasers is that you will get an interference pattern between the two beams.  The interference pattern will oscillate between bright and dark at the difference frequency of the two lasers (the beat note).  Since your eye can only see frequencies up to $\sim30\ \text{Hz}$ you will not generally be able to see the interference pattern.  If you use a lens to focus the two beams onto a fast photodiode, you can see this beat note on an oscilloscope or spectrum analyzer though.  
If your lasers are adjustable, then you can use this beat note between the two lasers to phase lock them to each other.  Doing so requires some knowledge of electronics and control theory, but it will lock the frequency of the two lasers together so that as one laser drifts the other follows identically.  If you phase lock the two lasers, then you will be able to see the interference pattern with your eye.
