The Doomsayer is a Chasind who has fled from the Korcari Wilds after seeing his family and clan killed by darkspawn. He is standing near the Village Chantry in Lothering, scaring some of the local villagers with his outbursts.
There is another Doomsayer in Redcliffe Village after the village has been defended successfully. He can be intimidated, killed, or left alone. There appears to be no XP granted, whichever option is chosen.
Involvement
The Doomsayer in Lothering can sense the taint that the Warden bears. He can be made to leave, or at least be quiet, by shaming, intimidating, or calming him. Dealing with him grants 100 XP. He will stay away until the party leaves and re-enters the area.
It is also possible to earn some money from this interaction. After talking with the Doomsayer, a villager will ask, "He was right, wasn't he? There's no hope for us..." Selecting "That's right. No hope for any of you fools!" will give the option to select "Give me your valuables, and your sorry lives may be spared." The party receives 45 
and 100 XP.
Trivia
- If you make him leave, then the villagers around him will also leave after the conversation is over. If you can steal and want to steal from them first, tell everyone to ignore the Doomsayer or tell him he's wasting your time. This will end the conversation with the Doomsayer, with the crowd (and Doomsayer) still there, giving you time to steal from them. Then you can talk to the Doomsayer again and make him leave.
- He can say to the female Warden that she and his wife share the same hair color.
Bugs
A few seconds after the Lothering Doomsayer has run off, his disembodied voice may be heard shouting that the darkspawn will "feast on the hearts of your children". Or alternately, "The evil will descend upon us."
Cutting behind the crowd and hugging the edge of the Chantry porch still triggers the cutscene, but can result in being teleported outside the wall by the edge of the stream and a little door along with the crowd and the Doomsayer. The only way out is past another wagon, angling against the edge of the stream to bypass the yoke. Your party won't follow you out of the area, but triggering a cutscene, entering a building, or running far enough away should teleport them all to you.