The spin cycle is making a terrible noise - the drum seems very loose and even makes a starnge sound when moving it by hand. Can I repair this myself?

If this is a Whirlpool manufactured TOP LOADER (such as Roper, Estate, Kenmore, Amana, and Frigidaire), you may have a damaged or broken motor coupling. Whirlpool manufactured top loading washers use a motor coupling between the drive motor and gearcase (transmission) in place of a drive belt. This configuration is known as "direct-drive". The coupling can break through normal wear and tear. Washing frequent loads of heavy items and reduce the life span of the coupler. Common symptoms include the following:

1. No spin or agitation.
2. Washer will fill and empty.
3. Drive motor still runs.
4. Strange rattling, grinding or clicking noise during agitation or spin cycles as the drum sits still.

If your washer is exhibiting these symptoms, then its probably a safe bet that the motor coupling is bad.

The following link explains how to replace one:

http://www.fixya.com/support/r3574231-replacing_a_motor_coupling

The part number for a replacement motor coupling is inlcuded in the link I provided. Replacements can be purchased at any of the following websites:

searspartsdirect.com
appliancepartspros.com
pcappliancerepair.com
repairclinic.com

All these sites are reputable and offer great service with competitive pricing, so shop and compare. The first three sites I have listed also included helpful exploded view parts illustrations to assist you with locating and properly identifying any parts you may need.