The short answer is: Yes, God hates some people. The long answer follows.
God loves everyone in some sense. But his love for the reprobate is not absolute. Rather, it is mixed with hatred. According to Scripture, God both loves and hates at the same time, though clearly in different senses. Certainly in some texts "hate" is used in a rhetorical/hyperbolic sense (e.g., Luke 14:26). But this is not usually what it means.
There are quite a number of passages in Scripture that say that God hates sinners, and there are good reasons, both literary and theological, that we interpret them to mean that he actually does despise sinners. Let's consider Psalm 5:4-6 first, where David wrote:
"For You are not a God who takes pleasure in wickedness; No evil dwells with You. The boastful shall not stand before Your eyes; You hate all who do iniquity. You destroy those who speak falsehood; The LORD abhors the man of bloodshed and deceit."
Many commentators have suggested that God's "hatred" here ought simply to be understood in contrast to his love. In other words, his hatred is simply a hyperbolic way of speaking of the absence of love. The problem is that the text itself does not suggest this meaning, and this meaning is not intuitive based on the content of the passage. Rather, it seems to me to be an entirely arbitrary suggestion that we take "hate" here in the same way it is used in Luke 14:26.
In passages such as Psalm 5, we don't simply have a random occurrence of "hate," or a mere poetic parallel, or an obviously hyperbolic use. What we have is a statement of hatred coupled with a description of what that hatred entails. In Psalm 5, in addition to hating and abhorring the wicked, God "destroys" them; they cannot stand in his presence. Now, unless we want to argue that being "destroyed" is simply being "not blessed," we've got a problem saying that God doesn't feel actual hatred toward these individuals. Sure, we could take the entire section as a rhetorical construct, but the fact remains that God actually will punish these sinners eternally in hell for their transgressions. He himself will subject them to torments because he is so angry with them. That's not merely motivated by an absence of love, and it certainly is not consistent with love acting on its own.
Besides, Luke 14:26 comes to us with the prior understanding that God doesn't really want us to hate our parents (Exod. 20:12). But Psalm 5:4-6 comes to us with the prior understanding that God actually does punish sinners in hell. Luke 14:26 works as a rhetorical device specifically because we know the statement is preposterous if interpreted simply. The same is not true of Psalm 5:4-6. On the contrary, we know that it speaks the truth about the fate of the wicked. As a result, we ought to expect it to speak the truth about the reason for the fate of the wicked, namely God's hatred.
Or consider Psalm 11:5-7:
"The Lord tests the righteous and the wicked, And the one who loves violence His soul hates. Upon the wicked He will rain snares; Fire and brimstone and burning wind will be the portion of their cup. For the Lord is righteous, He loves righteousness; The upright will behold His face."
Here God rains fire and brimstone on those he hates, and the reason he does so is that he is righteous. In other words, it is a praiseworthy quality in God that causes him to hate and to punish evildoers. Again, we don't have a rhetorical parallel; we have a purposeful description of a true threat.
Or Proverbs 6:16-19:
"There are six things which the Lord hates, Yes, seven which are an abomination to Him: Haughty eyes, a lying tongue, And hands that shed innocent blood, A heart that devises wicked plans, Feet that run rapidly to evil, A false witness who utters lies, And one who spreads strife among brothers."
Here we are told that God hates various things, some of which are sins, some of which are sinners. If God doesn't hate the sinners in the list, then he also doesn't hate the sins in the list. Presumably we can all agree that he hates the sins, so that we should also agree that he hates the sinners.
Perhaps the granddaddy of all passages describing God's hatred is Leviticus 26. In Leviticus 26:30, we are told that God's soul abhors those who continually break his covenant. Moreover, this is not a poetic passage; it is a description of the terms of the covenant. According to Leviticus 26:28-39, the covenant curses that will fall on those he hates include:
"I will act with wrathful hostility against you."
"You will eat the flesh of your sons and the flesh of your daughters you will eat."
"I then will destroy your high places, and cut down your incense altars, and heap your remains on the remains of your idols."
"I will lay waste your cities as well and will make your sanctuaries desolate."
"You ... I will scatter among the nations and will draw out a sword after you."
"As for those of you who may be left, I will also bring weakness into their hearts in the lands of their enemies. And the sound of a driven leaf will chase them, and even when no one is pursuing they will flee as though from the sword, and they will fall."
"You will perish among the nations, and your enemies' land will consume you."
"Those of you who may be left will rot away because of their iniquity in the lands of your enemies."
If that isn't a description of pure hatred, I don't know what is. And in fact, we know this isn't hyperbolic language because God did all these things to his people when they rebelled against him, and the Old Testament contains the record of it. Moreover, when Jesus returns, God will do even worse to those in hell.
Nevertheless, there are many commentators who argue that God hates no one. I just happen to think they're wrong on this one. And frankly, I'm not sure why we should want to think that God hates no one. After all, what kind of God sends people to hell when the underlying emotion he feels for them is love or apathy? I don't want that kind of love, and I don't believe that apathy takes such strong measures to obliterate those it supposedly "doesn't love."
Now, I should add that one reason many people try to argue that God doesn't hate anyone is their desire to defend God as non-capricious and non-malicious. Insofar as hatred is evil, God does not hate. He does not hate randomly or impulsively (i.e., he is not capricious); and he does not hate with evil motivation (i.e., he is not malicious). His hatred is earned by those he hates. It is his righteous response to their own evil. If we have to find another word for that than "hatred," that's okay, as long as we don't deny that he can't stand these people, that he doesn't want them in his presence, and that he wants to hurt them extremely badly, causing them immense and everlasting pain. Personally, I think "hatred" is a pretty good summary of God's feelings about them, but I am certainly open to other words if they do a better job avoiding implications of caprice and malice.
The problem this creates, of course, is that we have to say that God both hates and loves sinners. But as I implied at the beginning of this answer, that really isn't a problem. It is no contradiction to say that God hates them in one sense and loves them in another sense.
In fact, if we think about it, we can all come up with examples from our own lives of things we both love and hate. I hate getting shots because they scare me and they hurt, but I love what they do for my immune system. It is harder when we apply this idea to people, but not impossible. For instance, we are supposed to love our enemies, but most of us also hate them. We are capable of experiencing of a mixture of love and hate toward them, such as patience and longsuffering one the one hand, and a desire for God to bring just retribution on the other (Rev. 6:10).