Not necessarily. It all depends on the situation. For most blackouts you won't have to worry. However, if a large power surge occurs, such as when lighting strikes the powerlines, your computer might be in trouble. To keep your costly computer equipment safe, invest in a surge protector or, even better, a UPS (uniteruptable power supply).

As a matter of fact, if you are using your computer during a blackout, you could seriously damage your hard drive(s). Since most HDs spin at a rate of 7200 rpm (depending on type of connection and HD), if you were to completely remove the power, the heads of the HD would drop onto your platters in the HD and maybe cause physical damage to your HD, since the platters are rotating at a very fast speed. However, the use of a UPS is the best way to prevent this problem. I would suggest an APC that has enough volt/amps to support everything that will be using the battery. Just multiply the total watts of all the hardware and multiply by 1.4 to get the correct volt/amps.

I have to disagree with damaging the hard-drive when a blackout occurs. Modern hard-drive design has eliminated that effect. It is true the heads are tensioned by springs to contact the platters, and the 5400/7200/10000 rpm spinning of the disk cause the heads to "float" mere nanometers above those platters. However; when power is suddenly disconnected, the internal hard-drive circuitry senses this, by using a voltage threshold algorithm and sends the heads to their "parked" position. The power to accomplish this is derived by a combination of the remaining momentum of the platters, and remaining stored energy in capacitors located both in the hard drive and power supply. Yes, the power supply also. A Power supply does not instantenously black out due to filter capacitors on it's output. The hard-drive has sensed the loss of power way before the power supply has gone to zero output. All this is happening in milliseconds. The parking result is almost instantaneous. Layman terms used throughout this of course. Damage to hard-drives mainly come from moving the computer/hard-drive while the disk is running. This causes the head to "bump" the platter, and possibly damaging the sectors it contacts. This effect is cumulative and usually doesn't "wipe out" a hard-drive. It only reduces the area the OS can write to, reducing the disk's capacity. The only damage that should occur on a blackout in modern systems is as you've already mentioned - a loss of any data stored in memory which hasn't been written to the drive at the time.

You can buy batteries that will allow your computer to stay on for about 1hr after a blackout therefore giving you time to properly shut down