There is a very interesting paper in the latest early edition of PNAS, Hansen et al, Quantification of Global Gross Forest Cover Loss. (It should be noted that this is not James Hansen of NASA GISS, but rather Matthew Hansen of South Dakota State University). The paper uses satellite images in 2000 and 2005 to assess forest cover and forest cover loss between those years.
Firstly, the location of forests (which are defined as having at least 25% tree cover at least 5m in height) are as follows:
Note that these are not annual percentages - divide by five to get those (strictly, do the thing with the one fifth root, but dividing by five will be close enough for these values). Also, this is gross forest cover loss - they are looking for abrupt disappearances of the canopy, and not the gradual regrowth of forests that might be filling in elsewhere. So we don't get estimates of net forest loss/gain from this paper.
Overall, the gross forest cover loss is 0.6% annually which doesn't sound like a truly scary number (particularly when we don't know the regrowth rate). However, it's the regional variations and their causes that are most fascinating, and where there does seem to be some potential for alarm.
The largest losses are occurring in boreal forests (you can easily see them in Canada and Siberia and Scandinavia). And there, they estimate that 60% of the loss is due to fire, with 40% due to some mixture of logging and insect damage (which they cannot distinguish). For example, the mountain pine beetle outbreak in British Columbia is clearly visible on the global map. The boreal region is of course where climate change is greatest (the Arctic is warming about twice as fast as the planetary average), so this seems consistent with a story of climate-induced forest damage (though that's not an attribution the paper makes).
Elsewhere, the major hotspots of forest loss are in the Amazon and Indonesia/Malaysia, and this is primarily driven by logging and conversion of forest to other uses. In the United States, the major hotspots of forest loss are in the west, and also in the southeast, which is apparently being logged at a great rate. As a fraction of forested area, the US is losing forest faster than any other nation with large forests - 1.2% annually (again, on a gross basis). Canada is a close second at 1.06% annually (though most of that is inadvertent). At any rate, we shouldn't be doing too much preaching to Brazil (0.73%).
Update: here's a map of global temperature trends, 1901-2008, from NOAA data - you can clearly see that Canada and Siberia are amongst the areas experiencing the greatest change.