Most people I see comfortably opining on drone strikes seem to be doing so without the discomfort of thinking the issue through. My thought process is this:
Say the US were to find evidence that a Canadian terrorist group was planning an attack on the Joe Louis Arena. We would inform the Canadian government who would then go, arrest the terrorists and put them on trial. This seems to be what drone critics think should happen in countries like Pakistan, Yemen, and Somalia. There are some pretty obvious problems with that position.
Countries like Pakistan, Yemen, and Somalia all have weak, corrupt, ineffective governments. Naturally, they also have weak, corrupt, ineffective police forces. Normally, the US government doesn't care. The US government is responsible for US citizens, and Pakistan's problems are the responsibility of the Pakistani people's government. However, the US now perceives some groups within those countries as threats. We could give the Pakistani government all the info we like, but unlike Canada, we can't realistically expect that to result in the arrests of the terrorists. Even if we tried to give lots of support to their police forces, it is almost certain that the terrorists would be informed about any and all police movements (e.g. Bin Laden lived down the street from a Pakistani military academy.)
So what should we do?
Ignoring the threat is too great a political risk. If Pakistani terrorists executed so much as a single attack on US soil, you better believe the headlines would read: "Politicians knew of terrorist threat, failed to act."
No US law enforcement agency is effectively equipped to police Pakistan. We can't ask NYPD to go police the Pakistanis, that's stupid. The FBI is the best candidate, but their responsibilities are primarily investigative; the actual subduing of the terrorists is outside their purview.
The only other real option is some form of military action. Technically this violates Pakistan's sovereignty, but who cares? Pakistan is a weak government, it can't even police its own country. It's politicians may object, but it is not going to start a war with the US. Moreover, Pakistani terrorists not only kill lots of Pakistani civilians, but also are incredibly costly[1]. Therefore, many politicians will actually support the US's intervention, even if they have to publicly distance themselves. Obviously military intervention carries the risk of civilian casualties, but remember that the US government's responsibilities are towards US citizens. It is the Pakistani government's responsibility to protect Pakistanis, and it is a failing of the Pakistanis if they have not created a government capable of protecting them.
What sort of military intervention should we use? We could send in soldiers to try and arrest the terrorists, but that is slow, risky, and expensive (we need holding facilities, transportation, etc.) Drones are the obvious alternative. Not only are they cheap, they are pose about zero risk to US personnel. People mention that drones may create terrorists, but if we assume that Pakistani public opinion is proportional to the number of deaths, then terrorism (which has killed far more innocent Pakistanis than drones [2]) ought to be significantly less popular.
[1]http://en.wikipedia.org/wiki/Terrorism_in_Pakistan
[2]http://en.wikipedia.org/wiki/List_of_terrorist_incidents_in_...