I have seen a couple global studies using WGS84 as geographic reference, with the problem that the area of raster cells is not constant. Which reference system would you use for a global analysis in order to have a constant cell size?
What you're looking for is an equal-area projection, and ideally one which also partially preserves shape. In the past, I've used the USGS projection DSS to help guide these decisions, it'll walk you through a process of choosing a good projection. More generally, tools like Flex Projector and Tissot's Indicatrix should help guide a decision: they provide ways of assessing distortion. There's also an existing question on choosing a projection that may help you.
A favorite of mine for global analysis is Mollweide, which is widely supported in GIS packages and retains shape well enough to remain familiar.
Have a look at the paper "A COMPARISON OF EQUAL-AREA MAP PROJECTIONS FOR REGIONAL AND GLOBAL RASTER DATA" http://carto-research.er.usgs.gov/projection/pdf/nmdrs.usery.prn.pdf which should help answer your question.
It's a good question, because gridding lat-lon usually introduces tremendous distortions and often they can be avoided. However, the answer depends on the analysis. Not all analyses need equal cell sizes. Many times you can weight a grid calculation to compensate for variable cell sizes: the appropriate weighting factor is the cosine of the latitude. Given this possibility, which is usually easy to implement, you might want to weigh additional considerations in the balance, such as the desirability of a conformal projection. This would be especially useful when the analysis involves vector fields and their derivatives, which one would expect in climate models and the like.