Ah, yes, well. This is certainly a difficult question. And, for me, one a bit different than believing in God. I believe in God because I've experienced God. I've encountered something for which God is the only word I have. I have never met the devil, Lucifer, or Satan. So, all my thinking must be second-hand and, well, less certain. If I believe in the devil, it is not the same as believing in God, which is more like believing in you, because I've met you. And one might reasonably make the claim that there is no evil on earth that humans cannot ultimately cause. There is another word for Satan, and he is us, all our darker nature. All the rest is metaphor.
However, this has not been an acceptable explanation for most people throughout most of history. Everyone has an adversary, which is Satan's biblical role. It is not a stable or central identity. In Scripture, Satan evolves from a snake in the garden to prosecuting attorney to a mysterious tempter to an opposing power and the ultimate beastly evil at the end of time. Most of the things people have heard about Satan, such as the rebellion in heaven and Satan's reign in hell (rather than wandering the earth) are additions of Christian and other traditions, and are not biblical teaching, though we would note that most all orthodox Christianity has indeed believed in the existence of the devil, whatever the details.
But the point is that the scriptures, and especially the Gospels, strongly posit a vision of two kingdoms: the kingdom of God and the kingdom of this world, with the latter being given over to the adversary. The powers and principalities of this world are fallen, corrupt, and not ultimately to be trusted for human welfare and salvation; they are the opposition. They are the instruments and dominion of the enemy. Jesus didn't want you to go kill Caesar, but he did want you to know that Caesar might be playing for the other team. So, Jesus opposed the devil. Christ clearly saw a spiritual dimension of existence to which we moderns are not accustomed, and treated elements of it as cursed and abhorrent parts of the anti-kingdom, the one opposed to God -it's not entirely implausible that the anti-kingdom would have a king, who tempted Jesus in the wilderness.
So, with my own experience not being applicable, based on tradition and scripture, especially in the witness of Christ, I would say that yes, the devil does exist. The wandering adversary has effects in this world, though I cannot describe the devil in any detail and doubt that anyone can, and cannot say to what degree the devil could make anyone do anything. The other point that scripture makes that doesn't, in my opinion, get enough mention, is how weak the devil's position actually is in this world. It's all provisional, it's all at the pleasure of God and can be taken away at any time. Demons ask Christ for permission to do what they do, and similar powers seem entirely under the authority of the first apostles, whose mandate scripture does nothing to diminish. Now, this puts God and God's servants in an interesting relation to evil and its agents, but that's a whole other theological problem, and quite beyond my ken.
The larger point, I think, is that the devil is ultimately weak and seems to serve a similar function to Israel's enemies in the Old Testament: God permits the devil to have his say for a while so that our chastening and salvation can occur through the action of our faith. Satan does not persist because of Satan's great powers, but because of God's permission and evil's slippery and multiform nature. We're not going up against the Dark Lord Sauron here. It's more like we're confronting Grima Wormtongue of Tolkein fame, or even Gollum. So it's not, I think, that the devil made you do it, so much as that God allowed Satan to do something to us all for a little while, even as our choices remain our own.
There is by exceedingly widespread testimony a part of the universe far larger than ourselves that seems to be arrayed against, or at best indifferent to, human flourishing - be it individual or corporate. The Greeks called it Fate, moderns call it chance or randomness. But for people who take seriously the spiritual dimension of our lives, Satan might actually be a more accurate description, because that seems to be his role: the opponent, the snake in the garden, the worm in the apple, the bump in the night that reminds us that not everyone's on our side, that death is at our door, that our parents will not always be able to protect us - that we are frail and ultimately alone, that our lives are fragile, that nothing in this world will deliver us, and that we ultimately depend on God and God alone for our existence and salvation. That's the devil, doing the devil's work.