The AR4 SPM says on page 9:
"There is observational evidence for an increase in intense tropical cyclone activity in the North Atlantic since about 1970, correlated with increases of tropical sea surface temperatures. There are also suggestions of increased intense tropical cyclone activity in some other regions where concerns over data quality are greater. "
On page 8 in table SPM2 it is claimed that it is likely that there has been an increase in tropical cyclones since 1970, and more likely than not that this was due to human influence.
On page 15 they say that "Based on a range of models, it is likely that future tropical cyclones (typhoons and hurricanes) will become more intense, with larger peak wind speeds and more heavy precipitation associated with ongoing increases of tropical sea surface temperatures."
In fact, research shows no increase in the number or intensity of hurricanes hitting the USA (note in particular Table 5). A similar lack of trend was found in the Pacific by Wu, Yeung and Chang (2006); in fact in some areas this study found a significant downward trend in hurricane intensity.
A 1998 study by 11 experts in the field (see also here) "Tropical cyclones and global climate change", published in the Bulletin of the American Meteorological Society, stated in the abstract that "there is no clear evidence of long-term trends". Their conclusions included "there are no discernible trends in tropical cyclone number, intensity or location from historical data analyses" and "there is no evidence to suggest any major changes in the area or global location of tropical cyclone genesis in greenhouse conditions".
In 2005, a paper by Pielke et al, also in the Bulletin of the American Meteorological Society, concluded that "claims of linkages between global warming and hurricane impacts are premature for three reasons."
Not a single one of the four papers mentioned above is cited in the relevant chapter (chapter 3) of IPCC AR4. This is despite the fact that there is a five-page section (3.8.3) on tropical cyclones. The IPCC prefers to refer to papers by Emanuel (2005) and Webster et al (2005) that find in increase in intensity. Here we see again the familiar story of the IPCC referring to papers that support its agenda, while ignoring those that do not.
The IPCC does cite a paper by Klotzbach (2006), but does not mention its conclusions - "These findings are contradictory to the conclusions drawn by Emanuel  and Webster et al. . They do not support the argument that global TC
frequency, intensity and longevity have undergone increases in recent years." Instead, the IPCC authors illustrate their usual bias by making the unsubstantiated claim (twice) on page 306 that Klotzbach's 20-year data set is too short.
The latest data in 2009, from the Center for Ocean-Atmospheric Prediction Studies in Florida, shows that global tropical cyclone activity is currently at its lowest level in 30 years (see also discussion here). This confirms that the IPCC statements are wrong:
Some of this work is published: R. Maue, Northern Hemisphere tropical cyclone activity, Geophys. Res. Lett. 36, L05805 (2009).
It was the issue of false IPCC claims about increasing hurricane activity that led to the resignation from the IPCC of hurricane expert Dr Chris Landsea. Landsea had been an author on the IPCC's 2nd and 3rd reports, but resigned in 2005, saying that the IPCC had become politicized. He objected to lead author Kevin Trenberth giving a press conference saying that global warming would lead to more intense hurricanes. More on this in the next entry.