Does a calibration curve of absorbance vs concentration need to pass exactly through the origin?
Good answers, but it is almost never a good idea to force the intercept to zero. Unless there is a clearly justifiable and compelling reason to do so, it is better to let the data set 'vote' for itself and not impose a preference/bias/mandate. Among other things, forcing the intercept to zero changes the standard error of the slope, which is an important statistic.

Below is a screenshot of the result of using Excel's Data Analysis tool on a set of linear calibration data I collected in the past:



As shown, the intercept is -0.0541 and its standard error is 0.0352, so the t test statistic of the intercept, defined as intercept/(standard error of the intercept) = -1.537. The negative sign is irrelevant for present purposes, but the P-value is 0.264.

The null hypothesis for the intercept is that the true intercept, which is unknown, is zero. The alternative hypothesis (aka research hypothesis) is that the true intercept is either 1) not equal to zero or 2) not equal to zero, but in a known direction. The former is the 2-tailed option and the latter is the 1-tailed option. For intercepts, the 2-tailed option is most common and this would almost certainly be the case for a Beer's law plot. 

The P-value of 0.264 is much higher than the usual 0.05 value and this means that it would be quite risky to reject the null hypothesis based on the OLS analysis. In fact, the risk of mistakenly rejecting the null hypothesis, even though it was true, would be 26.4%. The confidence in the alternative hypothesis would be 100% - 26.4% = 73.6%, which is too little confidence for most people. Typically, you want P ≤ 0.05. Otherwise, it is too risky to 'jump ship' for the alternative hypothesis.

What does it mean? Well, the data resulted in a P-value of 26.4%, so the null hypothesis cannot prudently be rejected. But it is also not accepted: it still might be wrong, but the data did not show that. Replacing the intercept by zero would mean that a decision was made that the true intercept was zero, even though the analysis proved no such thing. It is not a good idea to pretend that the data showed what it did not show. Bottom line: the intercept should not be forced to zero unless there is a clear and compelling reasion to do so.