As Paul tells of the Gospel, he talks about things being revealed. He talks about the good in the righteousness of God being revealed in 1:17. Then he talks about the bad in the wrath of God being revealed in 1:18. But what would make a good and loving God reveal wrath? The answer is the ugly. That is, it is the ugly side of man ... the side that rejects God, His righteousness, and His Gospel. In fact, Paul makes mention of 3 different groups that brings the wrath of God:
Those who are UNGODLY. These are those who consciously determine to ignore the divine pattern. You often will hear individuals or congregations say, "We have restudied that.." That is a conscious effort to ignore God's pattern. Or, "I don't care what the Bible says, I think..."That is a conscious effort to ignore the divine pattern. Also, they practice what is foreign to the holy nature of God. For example, since God is loving, just, and compassionate, we are ungodly when we are unloving, unrighteous, not just and not compassionate.
Those who are UNRIGHTEOUS. These are those who determine to practice evil instead of good. God has put in place a moral law that allows mankind to like with mankind and still get along. Yet there are those who will go in the opposite direction of that. Isaiah warned of those who would call evil "good" and good "evil." In a day when killing is called choice, immorality is called lifestyle, use of narcotics is called recreation, and not honoring vows is called seeking happiness, Isaiah's warning is coming home to roost.
Those who are TRUTH SUPPRESSING. These are those making determined effort to bury the truth. Those who are hindering or holding back the spreading of truth. This is a very powerful image. They know it is truth and sot and cover it up so there will not see it. Verse 19 says God is making it evident (He does so because He wants all to be saved). These guys, however, are covering it up. Think of the guys still publishing debunked "proofs" of evolution. Think of the guys writing tracts who are purposefully leaving out the context of a verse.
What do all of these have in common? They are bringing God's wrath upon themselves. When we ignore God's word and live ungodly, when we practice evil instead of good, or when we intentionally try to suppress the truth from others, we are doing the same. It does not have to be that way. What do you want God to reveal to you?