On a line chart it can be done using a second data series. Here is an example.
Cells A14 & A15 contain the formula TODAY() to have the current date. Cell C15 has the formula MAX(B2:B13) so the line for the current date goes from zero to the largest value. In the Select Data dialog box, the Hidden and Empty Cell Setting has been changed as shown in the picture so that the blue line for the values is not broken due to it not having values in cells B14 and B15.