In the movie Sunshine, why does the Icarus ship even need a crew at all? Even with our current technology we are able to remotely send ships to (and land on) distant planets. So why couldn't the Icarus just have been targeted at the sun and flown remotely from Earth with no crew? The sun is a pretty big target, after all. This would be much more preferable especially when considering the volatile and unpredictable nature of human behavior. The crews always screw it up!
The Icarus mission is both far more expensive and far more important than that of any probe or lander...
The Icarus is uniquely expensive:
We've mined all Earth's fissile materials...
In other words, the two Icarus ships represent humanity's only chance to correct the problem with the Sun. The people of Earth have literally invested everything they have in these ships.
If something were to go wrong, such as a solar flare interfering with instrumentation or navigation, resulting in the Icarus "missing" the Sun, then all of our resources (and hopes) would have been wasted.
A crew is necessary to perform manual commands, overrides, and repairs to give the mission the best chance of succeeding.
Also, recall that the payload is unprecedented...
...with a mass equivalent to Manhattan Island.
If something went wrong in such a way that the device went off too close to Earth's atmosphere or too close to another planet like Mercury or Venus, life on Earth could be severely affected (directly or indirectly).
Having an expert on board who participated in the design of the device would be essential to give humanity at least a chance of averting a disaster of epic proportions.
Also, there is a distance at which there can be no effective communication between the Icarus and Earth-based control stations (due to solar interference):
All right, if no one's gonna say it, I'm going to. The solar wind reading is much higher than we'd anticipated at this distance. For the moment we can still send package messages back. High-frequency bursts will rise above interference...and the Moon Stations will be able to pick them up. But it's possible that within 24 hours we won't be able to communicate at all...We'll finally be on our own.
Given this reality, there is no feasible way for corrections, split-second or otherwise, to be made remotely.
In a sense, the Icarus mission is the most important human undertaking in the history of civilization, in-universe. Having a small group of individuals on board to help ensure that it goes as planned seems logical.
For one thing, communication cuts out when within a certain distance of the sun due to radiation. Given that they wouldn't be able to communicate with it, it makes sense to have humans on board that can continue to guide the craft and make sure the bomb detonates correctly. Since this is the last hope for humanity, it seems worth it to have the extra insurance of a human crew.
Also, although it's not mentioned in the movie, the mechanism for the sun's dimming is a Q-ball: http://scienceandfilm.org/articles/188/separating-the-science-from-the-fiction-in-sunshine. It's a localized phenomenon so they would have to detect and hit it precisely, which could be beyond the ability of a remotely operated craft, particularly once it's outside of communication range.