Yes, your votes count. Every campaign manager on both sides of the aisle can recount elections that were won or lost with very slim majorities or in some cases pluralities. I have seen elections come down to a margin of less than 1 percent.
No, the system is not perfect. The U.S. presidential election has actually had several “anomalies”. John Quincy Adams took the office for one term despite coming in second in the popular vote and the electoral college when the electoral collage deadlocked and the House of Representatives choose the President. Ruthorford B. Hayes “won” after a Congressional dispute over who should get the electoral votes from several southern states was settled by a Congressional Commission which agreed that federal troops would be withdrawn from the south (allowing the defacto repeal of most reconstruction initiatives) if those states would allow their electoral votes to go to Hayes. Benjamin Harrison lost the popular vote by 100,000 but won the electoral college by 233 to 168. John F. Kennedy won the crucial electoral votes of Illinois when Cook county’s paper ballots were counted late and ballots from heavily Republican precincts were found floating in the Chicago river the next day. (Nixon decided not to contest the election on the grounds that it would be too divisive for the nation.) And yes, in 2000 Al Gore won the popular vote by about 500,000 while losing the electoral college vote. However, it should be noted that ALL subsequent recounts of the Florida votes, including 2 by the press using data gathered under the Freedom Of Information Act showed that Bush had in fact won the electoral votes in Florida legally.
Also, the “faithless elector” who does not follow the vote of his or her state is a myth. In the entire history of the electoral college their have been only a handful (I believe less than a dozen) who did not cast their electoral ballot for the winner of the popular vote in their state.
So yes your vote counts. Is it necessary? If the Democrat turnout in Ohio had been about 1 percent higher in 2000, Florida’s electoral votes would have been meaningless.