Build a small, lightweight trunk for a bicycle that you can also lock. This cost me about $10.
Step 1: Obtain Trunkish Object
I used a 16" toolbox from Lowes, which cost me about $8. The brand is "WorkForce" (very tough sounding, no?) and it has a metal clasp, pass-through for a lock, and is made of plastic - all traits it needs for this project.
Step 2: Drill Holes
I lined up the tool box where I wanted it to be on the luggage rack, and marked where it passed the cross members of the rack. These are where the trunk will attach to the rack. I used cable ties (about $2 for a small bag) to fix it to the rack.
Step 3: String It Up
I drilled 12 holes in all. That's 3 rows, with 2 holes on each side. I laced the cable ties through these holes, leaving plenty of room on each end to tighten them. Once they were in, I lined it back up on the rack, and tightened them down.
Step 4: Enjoy
Once the ties were tightened completely, I snipped off the ends so it would look a little cleaner and less...you know...cable-tied. This certainly doesn't make this the most secure system in the world (anyone who wanted could slice these ties and take the whole box), but ot's more of a method of helping honest people stay honest. I don't leave anyhting very valuable in there for long periods of time (like outside my building all day), but it works well when I go into the bar for a drink, but don't want to carry around my blockbuster movies.