I hate to say it but your vote probably won't make a huge difference in the results if it's a solidly Republican state.
However, it does contribute to the overall popular vote of a candidate. Since everyone has the mentality that it doesn't make a difference, it makes it very difficult for the state to flip. If everyone in the minority decides to vote, though the candidate might not win, it will increase the popular vote of the candidate.
Example: Utah, 2016
For the record, the only states that hasn't flipped since 1972 are Alaska, D.C., Idaho, Kansas, Nebraska, North Dakota, Oklahoma, South Dakota, Utah and Wyoming.
But, in this election, some pundits did say that Utah might be contested, though it's a solid Republican state. So, even if it might not have a large chance of flipping since Trump is still leading, there is still a change of flipping.
Example: North Carolina, 2008
Also, North Carolina is also considered a solid Republican state, but Obama won it in 2008 anyway.
Example: 1992 Presidential Election
Also, in addition to the states listed above, here are some example of states that are considered solid in the past but flipped after the 1992 landslide victory for the Democrats: California, Connecticut, Delaware, Illinois, Maine, Maryland, Massachusetts, Michigan, New Jersey, New Mexico, Vermont.
At that time, people probably won't thought that their votes counts a lot but it did.
So, in conclusion, I do think that voting matters even if it might not affect this year's election. It might be useful, who knows that Obama would have won North Carolina in 2008?