I am aware of the current urge for self-diagnostization among historians (and other scholars in similar fields), the need to put a label on our own time (see Francis Fukuyama and the like). But are there any other significant trends in historical research today?
Yes, but I think right now we are reappraising the many trends that have come to light or have gotten more press since the early 1990s.
'The Cultural Turn' is probably still the most prevalent and widely used by scholars today. It originated in the 1970s and continues today. In simple terms, it's a reappraisal of past events utilizing cultural cues and seeking understanding through an discursive analysis of texts, images, songs (a sort of text, obviously), art and other vestiges of cultural significance. Letters, poetry, diaries - all of these help lend an analytical and often more personal touch to history. This, as distinguished from the social histories which focus on statistical analysis, sheets of data, population census (censi? what's the plural of census?) and the like in a view to discover wider trends and the larger picture.
Marxist historians kind of 'lost out' after the fall of the USSR, but not fully. Many marxist views are still seen as very valid. An example of a Marxist view of history would be that the forces which brought about the French Revolution lie within a class identity struggle and the means of production being held by a small minority of powerful aristocrats.
But what really has been in vogue with many academics lately are the post-modern or post-colonial theories. Gendered history is a body of theory I use very often in my writing and research. Foucaultian theory is very analytical and seeks to understand the relationships of power and the dynamic of sexualism and power in inter- and intra- personal and national(statist) relationships. The use of power psychologically, physically or mentally is often used to better attempt to understand everything from war to genocide to terrorism to domestic politics (and often all at once.)
Post-colonial theories focus on all kinds of relationships and identity structures, but mostly upon the power relationships between former colonies and colonizers and the struggle to establish, reestablish or restructure a national, political, religious, social or cultural (often times all of the above at once) identity in the face of a new and uncertain future. Post-colonial histories of India, for example, may attempt to reconcile an Indian past with the disparate histories that exist - that of the colonized Indians/Pakis/etc. and that of the people of India, with the colonizers as an afterthought. Not all histories of India need focus on the effects of the British. Or need be written from the view that there were abrupt and violent bookends to India's history - pre british rule, british rule, and post british rule. These bookends may be the most descriptive - but they are not necessarily the only form in which to structure the narrative.
Post-modern theories kind of envelop all of the above. If the 'modern' is said to have evolved from the Enlightenment and the attempt to use rationalism and understand better the human struggle within a sense of time and space, post-modernism is a reflection of these theories and an attempt to reestablish a narrative, or to break apart that narrative, into something new in hopes that we can understand what was previously hidden. Feminist history, for instance, is often broken up into many 'waves', of which the earlier waves of feminism focused on the issue of treating women as individual persons, who need not be seen as merely an appendage of their male counterparts. This has evolved to a point now where people are seeking to understand if there is a need to see gender, or sex at all. Seeking to see women as not an equal foil to men, but as somehow fluid. Where man or woman is not necessarily restricted to the gender or sexuality of themselves. Not to go off on a feminist rant - but you see the point.
History writing today in the deep circles of academics are looking at these issues and sometimes expanding, sometimes negating, but always reinvestigating these theories, and attempting to use these theories to reanalyze previous issues, especially contentious ones.
Personally, I use a significant amount of (some new, some old) sociology and cognitive and social psychology theories (need to belong theory, 'good copy' theory, religion as a social identity theory, perceived depravation theories etc.) to analyze the relationships between perpetrators of and victims of political violence, especially in regards to acts of suicide terrorism. None of these theories were overtly written to understand terrorism or even violence, but historians today are finding these theories in cross-disciplinary studies and seeking uses outside of their intended fields.
Hope this helps.