1 Cor. 5:4-5. Looks like the church turned the erring brother over to Satan via imprecatory prayer.
1 Cor. 16:22. A solemn imprecation at the end of the same epistle, reminiscent of...
Gal. 1:8-9. Paul's imprecation on false preachers.
1 Tim. 1:20. Paul evidently delivered these hereticks (who may have been saved--cf. 2 Tim. 2:16-21) over to Satan for judgment by prayer, since prayer (including intercession) is found in the context (2:1-7). Note that the goal was correction ("that they may learn"), leading me to believe that Hymenaeus, this Alexander, and Philetus (2 Tim. 2:17) were professing believers.
2 Tim. 4:14-16. Here you have imprecation (vv. 14-15) followed by intercession (4:16). Paul wishes judgment on an opponent of the truth (Alexander the coppersmith), yet asks God to be merciful to brethren who wouldn't stand with him at Caesar's judgment seat. In one case, you have someone willfully opposing the truth (Gal. 5:12--yet another imprecation!), while in the other you have some weakly refusing to stand up for it. Very different heart conditions, both requiring prayer.
Personally, I'm hardly ever inclined to pray imprecatorily, since it seems that our primary goal in prayer is to seek men's salvation and growth (1 Tim. 2:1-6; Gal. 4:19; Col. 4:12; etc.). I do pray for God to correct people, saved or lost, but I don't find myself inclined to ask God to judge them.
One thing that all of the imprecations above have in common is that they're from apostolic times, and only 1 Cor. 5 deals with a church; the rest are Paul's personal imprecations against hereticks or opponents of the truth. So I'm more inclined to leave the imprecation back in those days, vs. employ it today.
Readers, I welcome your feedback on this, since I'm personally not aware of much teaching on it. I do not consider imprecatory prayers from the old testament, the gospels, or Acts 1-8, as examples for the body of Christ (BOC), since all of those periods fall under the kingdom program and are not doctrinally applicable to the BOC.
