Yes of course the Bible applies today, from Genesis to Revelation. For Paul wrote in 2 Tim. 3:14-17, "But as for you, continue in what you have learned and have become convinced of, because you know those from whom you learned it, 15 and how from infancy you have known the holy Scriptures, which are able to make you wise for salvation through faith in Christ Jesus. 16 All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, 17 so that the man of God may be thoroughly equipped for every good work."
Furthermore, Paul wrote in Romans 4:18-24, "Against all hope, Abraham in hope believed and so became the father of many nations, just as it had been said to him, "So shall your offspring be." 19 Without weakening in his faith, he faced the fact that his body was as good as dead--since he was about a hundred years old--and that Sarah's womb was also dead. 20 Yet he did not waver through unbelief regarding the promise of God, but was strengthened in his faith and gave glory to God, 21 being fully persuaded that God had power to do what he had promised. 22 This is why "it was credited to him as righteousness." 23 The words "it was credited to him" were written not for him alone, 24 but also for us, to whom God will credit righteousness--for us who believe in him who raised Jesus our Lord from the dead."
Moreover, Paul wrote in 1 Cor. 10:1-11, "For I do not want you to be ignorant of the fact, brothers, that our forefathers were all under the cloud and that they all passed through the sea. 2 They were all baptized into Moses in the cloud and in the sea. 3 They all ate the same spiritual food 4 and drank the same spiritual drink; for they drank from the spiritual rock that accompanied them, and that rock was Christ. 5 Nevertheless, God was not pleased with most of them; their bodies were scattered over the desert. 6 Now these things occurred as examples to keep us from setting our hearts on evil things as they did. 7 Do not be idolaters, as some of them were; as it is written: "The people sat down to eat and drink and got up to indulge in pagan revelry." 8 We should not commit sexual immorality, as some of them did--and in one day twenty-three thousand of them died. 9 We should not test the Lord, as some of them did--and were killed by snakes. 10 And do not grumble, as some of them did--and were killed by the destroying angel. 11 These things happened to them as examples and were written down as warnings for us, on whom the fulfillment of the ages has come."
Therefore, the Bible does indeed apply to us today, and so this means that sins such as fornication, audultery, homesexuality and so on apply to us today also.