For any software project, there's always something new to research. Even if the flood of new technology suddenly freezes, most projects would still struggle just to catch up to the existing technology. While a lot of small to mid-size departments don't have dedicated research teams (or even tasks), here are some ideas to subtly incorporate research items into your schedule.
Focus on small, concrete tasks that management cares about. A web app probably cares more about research JQuery or Silverlight than it cares about the WinForms DataGrid, or something ambiguous like "incorporating web best practices" (what does that practically mean?)
Emphasize the low-hanging fruit with the highest return - Not all research tasks are equal. A SQL static code analyzer (which benefits everyone on the team) may be far more profitable than some crusade to make sure no-one uses Hungarian notation n C#.
Piggyback off of existing assignments. If you're implementing an Aspx page, it may be the time to investigate Ajax, JQuery, or even something smaller like just JSON - you'd essentially have "the wind at your back". You could research an unrelated task, like hosting your build process on virtual machines, but you'd be doing it all alone, without the support of your current assignments.
Focus on just one or two things at a time. You could easily list 50 things to do - new technologies, tools, refactoring, open-source projects, controls to integrate, upgrading your framework, testing, automation, code generation, etc... If you juggle too much, it will all crash and you'll have nothing.
Finish what you start; Actually deliver something - "A bird in the hand is worth two in the bush." For many departments, the thinking is it's better to have a weak solution that's completed (and hence usable - i.e you have something), than a powerful solution that's "still in progress" (and hence unusable - i.e. you have nothing.). The workplace is ablaze with buzzwords. Anyone can spew forth buzzwords or suggest grandiose visions, but at the end of the day - management cares about things that are actually done.
Work incrementally - Management may initially not allot 4 weeks to research how Ajax benefits your web app, but you could spend a day here integrating it, a day there using an update panel, another day later pulling in the Ajax Control Toolkit. Yes, it's slower, but it's better than nothing.
Establish a track record to "earn" bigger opportunities - As you gradually get research items actually completed, you'll become more credible, and will therefore probably be given more opportunity to research bigger tasks. For example, an unknown new-hire may be allowed to "explore" for a day, but a credible senior developer - who's already delivered many successful features - may be allowed to explore a research task for weeks.