To anyone who's ever asked a kid to sit on a 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 clear plastic bag; seal the bag; and then roll it to squeeze out the air, which compresses your clothes remarkably well.
Several manufacturers make these 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". The plastic bags are reusable, trip after trip.
Check several "Space Saver" types of travel bags
.
A second style of product works by actually vacuuming out the air (using a standard vacuum). For example, see this Space Bag Vacuum Seal Storage Bags
.

