Would it be any concern if we find correlation between intercept and other regression coefficients? During a multiple linear regression analysis, I found correlation between intercept (beta-0) and two of the other regression coefficients. Is there any problem or concern in this case? If no, please explain me why.

Such correlations are guaranteed if you have not standardized your predictors to take the value 0 at their means. However, this correlation is not really a mathematical/statistical problem, per se, but it may be easier to interpret the coefficients if you first standardize the variables. 
Therefore, the short answer is no, such a correlation is not a problem, its just the interpretation. See this link as well for a good discussion on this issue. The reason the correlation is not a problem, statistically, is that standardizing is a linear transformation (add/multiply by a constant), which should not affect how well the line fits. As a concrete example...a linear regression of, say, Reaction Rate vs Temperature, (for some chemical reaction) should not depend on the choice of temperature units (Kelvin, Celsius, Farenheit). Essentially, the units you express a relationship in should not affet the accuracy or validity of your linear regression, since different units of some property (e.g., length, temp, time) are related to each other via a linear transformation, and it would make no sense for a particular, arbitrary set of units to yield more accuracy than another set of units.
