I'm sure our first answer is "No, of course not." (Even if we are secretly or subconsciously thinking God must like Joe Schmo better than me because Joe gets all the breaks.)
But it all depends on how we define "favorites."
God loves all people the same, saved or not. There is nothing we can do to make God love us more, and there is nothing we can do to make God love us less. He has proved His love for the whole world by sending His sinless Son Jesus to die on the cross in our place--while we were yet sinners. And whosoever will may come to Him to have life. Furthermore, whatever God has done for me, He will do for you. This isn't to say that He treats everyone identically, because no two people are called to identical lives, including identical twins. If God didn't relate to you as the unique human He made you to be, then you wouldn't feel very seen, or as if the relationship were personal, would you? So I don't get a horse just because Joe Schmo got a horse, for example, but the promises of God in Scripture, and the supply of all my needs according to His riches in glory, are mine just as much as anybody's, if I belong to Him. To further make our point, we often quote Romans 2:11--"God is no respecter of persons." The Amplified 2015 version says it like this: "For God shows no partiality [no arbitrary favoritism; with Him one person is not more important than another]." It's good to note, though, that this is in the context of a discussion about salvation and judgment, whether under the Law or apart from the Law. As recorded in Acts 10:34, Peter speaks about his new understanding that God doesn't show partiality to people--but again, in the context of Gentiles no longer being unclean in the eyes of Jews. God is not willing that any should perish, but that all should come to repentance (2 Peter 3:9). Also, because favoritism is shown in the Bible to be sin, we can know God doesn't practice it. James 2:1-9, for example, warns Christians against showing favoritism (partiality, prejudice) on the basis of poverty or riches. Leviticus 19:15 reads similarly.
But wait.
Is there a difference between favoritism and favor(ite)? Yes, there is. Favoritism is defined as unfair or prejudicial preference. A favorite, on the other hand, is simply a preferred thing, with no connotation of disadvantage or harm to anyone or anything else. And let's carry this a step further: What if, instead of defining favorite as "someone who is loved/liked better than others," we define it as "a recipient of favor"? Someone who has favor is literally a favor"ite". Do people have, or can they gain, favor with God? Yes.
Psalm 5:12 says, "For You, O Lord, bless the righteous man [the one who is in right standing with you]; You surround him with favor as with a shield" (AMP 2015). Who is given (surrounded by; isn't that wonderful?) favor, according to this verse? The righteous person, and we Christians know we are righteous in Christ. Therefore, believers have God's favor. In Psalm 30:5, David urges "godly ones" to remember that "His anger is but for a moment, His favor is for a lifetime." Psalm 84:11 tells us, "For the Lord God is a sun and shield; the Lord bestows grace and favor and honor; no good thing will He withhold from those who walk uprightly." Again, as we walk uprightly, set apart (holy) for Him, we gain God's favor. Psalm 90:17 records that Moses prayed, "And let the [gracious] favor of the Lord our God be on us; confirm for us the works of our hands--yes, confirm the works of our hands." Here, concluding a prayer about the eternity of God and the fleeting life of man, Moses asks for favor that our short lives may have meaning on the earth. Proverbs 3:4, discussing the rewards of wisdom, exhorts, "So find favor and high esteem in the sight of God and man." The passage implies that we do so by trusting in the Lord with all our heart and keeping his precepts. Proverbs 18:22 is quite specific. It states that a man who finds a wife obtains favor from the Lord. There are other passages that imply God's favor upon people without necessarily using that word. One is 2 Chronicles 16:9--"For the eyes of the Lord move to and fro throughout the earth so that He may support those whose heart is completely His" (AMP 2015). Most translations say He's looking to strengthen those who are His. Scripture is clear that when we belong to God, and when we furthermore walk uprightly and devote ourselves completely to Him, we obtain favor with Him. And in that sense we are favor"ites"--people who have received favor.
It's true that splitting hairs on definitions the way I've done here may not always be practical in normal conversation. We tend to equate favoritism with having a favorite, or take favorite to mean "someone who is loved/liked better than others." We do need to be careful of the impression we are giving when we use words. However, to the question "Does God have favorites?" in a very real sense it is right to answer, "Yes. Yes, He does. And if you belong to Him through Jesus Christ, you, too, can be His favor"ite".