Yes demons (evil spirits) exist today, as they have since satan and his minions of fallen angels were thrown down from heaven.

Revelation 12:3-4
The Red Dragon, Satan
3Then another sign appeared in heaven: and behold, a great red dragon having seven heads and ten horns, and on his heads were seven diadems. 4And his tail swept away a third of the stars of heaven and threw them to the earth And the dragon stood before the woman who was about to give birth, so that when she gave birth he might devour her child.

Revelation 12:7-13
The Angel, Michael
7And there was war in heaven, Michael and his angels waging war with the dragon The dragon and his angels waged war, 8and they were not strong enough, and there was no longer a place found for them in heaven. 9And the great dragon was thrown down, the serpent of old who is called the devil and Satan, who deceives the whole world; he was thrown down to the earth, and his angels were thrown down with him. 10Then I heard a loud voice in heaven, saying, "Now the salvation, and the power, and the kingdom of our God and the authority of His Christ have come, for the accuser of our brethren has been thrown down, he who accuses them before our God day and night. 11"And they overcame him because of the blood of the Lamb and because of the word of their testimony, and they did not love their life even when faced with death. 12"For this reason, rejoice, O heavens and you who dwell in them Woe to the earth and the sea, because the devil has come down to you, having great wrath, knowing that he has only a short time." 13And when the dragon saw that he was thrown down to the earth, he persecuted the woman who gave birth to the male child.

I have personally encountered a demon and an angel, and I have witnessed people possessed and oppressed by a demon or demons and I have seen people delivered from possession and oppression.

Ephesians 6:10-20
The Armor of God
10Finally, be strong in the Lord and in the strength of His might. 11Put on the full armor of God, so that you will be able to stand firm against the schemes of the devil. 12For our struggle is not against flesh and blood, but against the rulers, against the powers, against the world forces of this darkness, against the spiritual forces of wickedness in the heavenly places. 13Therefore, take up the full armor of God, so that you will be able to resist in the evil day, and having done everything, to stand firm. 14Stand firm therefore, HAVING GIRDED YOUR LOINS WITH TRUTH, and HAVING PUT ON THE BREASTPLATE OF RIGHTEOUSNESS, 15and having shod YOUR FEET WITH THE PREPARATION OF THE GOSPEL OF PEACE; 16in addition to all, taking up the shield of faith with which you will be able to extinguish all the flaming arrows of the evil one. 17And take THE HELMET OF SALVATION, and the sword of the Spirit, which is the word of God. 18With all prayer and petition pray at all times in the Spirit, and with this in view, be on the alert with all perseverance and petition for all the saints, 19and pray on my behalf, that utterance may be given to me in the opening of my mouth, to make known with boldness the mystery of the gospel, 20for which I am an ambassador in chains; that in proclaiming it I may speak boldly, as I ought to speak. 21But that you also may know about my circumstances, how I am doing, Tychicus, the beloved brother and faithful minister in the Lord, will make everything known to you. 22I have sent him to you for this very purpose, so that you may know about us, and that he may comfort your hearts. 23Peace be to the brethren, and love with faith, from God the Father and the Lord Jesus Christ. 24Grace be with all those who love our Lord Jesus Christ with incorruptible love.