Managing each person's work as an explicit queue (rather than a loosely prioritized list) is something we're talking about here (and would make a great plugin: maybe request it on the plugin ideas page: http://fogbugz.stackexchange.com/questions/1158/plugin-ideas-forum-what-are-your-top-plugin-ideas-and-requests/1159?).
I find that a filter "All open cases in [Project] that are active in milestone [Next Milestone], sorted by Assigned To sorted by Milestone sorted by Priority" gives a pretty good idea if you're using priorities.
If that doesn't do the trick for you, then either adapting the Project Backlog plugin (the code is in Plugins/examples on your FogBugz install) would probably be the easiest route for making something really slick. Failing that, using the Custom Fields plugin to add a "Next Up" field or a "My Queue" field might suffice.
Finally, for an individual, you can create a queue using the 'Starred' feature and reordering your 'Starred' items, but that will only be visible to you.