I definitely keep them. Tag and bag em. I even have a page on my iPad of my string inventory. That way I can keep up with what I have available. Why? Because different strings sound different on different ukes. As a result, I have a drawer full of bagged strings. It's paid off on several occasions.
Here's how:
1. It allows me to experiment. For example - I have an 8 string baritone that normally is strung, dD,gG,BB,EE. I happened to have a set of Guadalupe strings designed to tune a bari GCEA, except an octave lower. Since I had this lower g in my string drawer, I put it on the 8 string Bari, and wowzer, it made a huge difference.
2. In the case of breakage - I simply go to the drawer and find a suitable replacement. Its happened at least twice.
3. It provides flexibility. I've often switched from Low G to Hi G (and back again) trying to get the most out of each instrument. Or sometimes, I Frankenstein a set - using an A string from one set along with a C string from another again in the attempt to get a certain sound out of an instrument.
4. It sets me up for a future uke. Once, I ended up selling a Concert, then a year later, received one in a trade. Its strings weren't so hot - but fortunately, I had saved some concert strings and I was able to restring the uke as I thought best.