Can blackouts affect my Xbox 360?

Solution 1:

It can affect the power source, yes. The most likely cause is a power surge that can affect electrical equipment and damage electrical systems, such as power supply, or the Xbox itself.

From wikipedia on power outages

Computer systems and other electronic devices containing logic circuitry are susceptible to data loss or hardware damage that can be caused by the sudden loss of power. These can include data networking equipment, video projectors, alarm systems as well as computers. To protect against this, the use of an uninterruptible power supply or UPS can provide a constant flow of electricity if a primary power supply becomes unavailable for a short period of time. To protect against surges (events where voltages increase for a few seconds), which can damage hardware when power is restored, a special device called a surge protector that absorbs the excess voltage can be used.

As the excerpt states, a Power-Surge protection power board can help avoid this problem. Plugging it straight into the wall or a regular power board leaves your devices susceptible to damage.