To anyone who'se ever asked her kid to sit on her suitcase so she can zip it shut: maybe you should try these compression-style plastic storage bags.
Here's the concept: put clothes into a reusable clear plastic bag; seal the bag; and roll it to squeeze out the air, and compress your stuff.
Several manufacturers make similar products, and typically sell a set of four or more bags in two sizes, such as 14" x 20" for "medium" and 18" x 23" for "large".
- Compare several "Space Saver" type travel bags
A second style of product works by actually vacuuming out the air (using a standard vacuum). For example:

