Have there been any large movements in philosophy that have developed recently (like, say, in the past 30 years or so)? The latest non-political philosophy that I tend to hear about as a non-philosopher is from the first half of the 20th century.
In the last thirty years or so the most important questions in analytic philosophy (by far the dominant brand of academic philosophy) have concerned philosophy of mind. The issues in question are many. As a general rule, philosophers have been interested in what of what the mind consists and what it is ontologically. 'Movements' exist on all sides of this question;the most popular is probably functionalism. Functionalism states that we must identify mental states in terms of there functions; 'fear' is just that state that causes people to act fearfully (run away, look scared, so on and so forth). Contrast this, for instance, with any theory that would hold that a mental state is a given mental state by virtue of being identical to a brain state.
Philosophy of mind has existed for a while (e.g. Descartes's dualism). In contrast, the serious study of modality has only arisen in the last forty years, driven mainly by the brilliant works of David Lewis (probably the most important philosopher of the latter 20th century). Modal propositions are those concerning what is possible and what is necessary (rather than what, as a matter of fact, is). For instance, counterfactual propositions like 'Were I to quit my job, I would lose my house'. David Lewis thinks that the truth of such propositions is dependent on what occurs in 'possible worlds'; that counterfactual proposition is true if and only if in the closest possible world to the actual world in which I do quit my job, I lose my house. This analysis, broadly speaking, has become accepted.
It is a very useful tool of analysis. For instance, take definition of knowledge. In 1963 a man called Edmund Gettier wrote a paper which made it clear that knowledge could not be justified true belief (the then paradigmatic definition). For the last forty years the implications of this have been worked out thoroughly in the academic literature spawning different positions the number and elegance of which I could not possible do justice to here. One particularly lucrative solution, however, has been to give a counterfactual account of knowledge. For instance, and account of 'S knows P' (being true) as including 'If S were to believe P, P would be true. Such accounts require an understanding of modality (in my opinion) to be illuminating.
There are many other issues that have risen to the fore in the recent past. For the last two decades moral realism has inexorably gained ground in academia; most academic philosophers now believe that moral statements are non-relative propositional statements which can be true; there are moral facts (some things are right, some wrong).In the 50s, 60s and 70s most philosophers tended to be noncognitivists; they though moral statements were just expressions of opinion.
In political philosophy liberal egalitarianism has established for itself by far the dominant position in academia. This is the theory that a state is just if and only if its citizens have 'liberal rights' and (in some substantive way) are materially equal. It's fair to say that socialism has been somewhat subsumed by liberal egalitarianism and libertarianism thoroughly discredited (although that is not to say laughed out of town).
So that's a smattering of things that have happened in modern philosophy. I have barely touched the iceberg*, really. In mereology (the study of parthood) fascinating paradoxes have been postulated and (perhaps) solved. In logic we have progressed by leaps and bounds and in normative ethics deeper and more satisfying theories have flourished. I could go on. What I mean to do in the above is give you (or any reader) a rough feel for the progress in modern day philosophy.
It is possible that the above is not what you meant by 'movements'. You wanted something grand and sweeping like Hegel or Heidegger's work. If so, you will have trouble finding anything
quite like that. Continental philosophy has produced many grand and sweeping (and deeply flawed) theories of life, the universe and everything. Analytical philosophers are not so interested in this endeavor; they tend to wish to apply the tools of logic and reason to problems in a detached way. Worldwide, around 95% of philosophy departments (and certainly every pre-eminient one) would describes itself as analytic.
*If you find any of the subjects I touch upon interesting, I am perfectly willing to go to more detail.
