If you drop the intercept, then instead of getting k-1 coefficients representing how different from the baseline each of those conditions is, you will instead get k coefficients representing how different from 0 each of those conditions is. Either one is possible, it just depends what's relevant to the hypothesis you're trying to test. In my case, I'm usually more interested in comparing each condition to some baseline condition than I am in comparing each condition to 0.

Thank you sir. If it depends on which approach can be more relevant to my objective, I just want know the validation of dropping the intercept?

Off the top of my head, I'm not sure of papers that report an analysis without an intercept or that directly discuss the merits or drawbacks of using this method. But you can inspect the models and do model comparison to see that a model without an intercept has the same fit as a model with, just different interpretations for the coefficients (see sample R code below). With dummy coding, in a model with the intercept then the intercept is the reference condition and each other coefficient is a comparison against the reference condition; without the intercept, each coefficient is a comparison against 0, and you can see that the coefficient for what would be the reference condition is exactly the same as the coefficient for the intercept in the other model.

summary( with_intercept