Apparently the most venomous spider is the Brazilian wandering spider (Phoneutria spp.). Phoneutria nigriventer's extreme toxicity in a table showing that the amount necessary to kill a 20gm mouse was only .006mg (intravenously) and .0134 subcutaneously as compared to Latrodectus mactans (Black Widow) at 0.110 and 0.2 respectively. Recent studies suggest that these spiders only inject venom in approximately one-third of their bites and may only inject a small amount in another third. The evidence, so far, clearly shows that both P. nigriventer and P. fera (on the photo) are extremely dangerous.
The funnel web spiders are another very venomous genus. Atrax robustus (on the photo) and Atrax formidabilis arguably are the most venomous and dangerous spiders in the world according with AFPMB.
The widow spiders are very dangerous too. The venom is not as potent as in the case of the two genuses above, but the evidence shows that there is comparable amount of deaths and health problems caused by these spiders. Relatively to the most of the spiders their venom is still very potent, (15 times more potent than that of the rattlesnakes; it is also reported to be much more potent than the venom of cobras and coral snakes). For Latrodectus mactans the amount of venom necessary to kill a 20 gm mouse was 0.110 mg (intravenously) and 0.2 mg subcutaneously. 63 deaths were reported in the United States between 1950 and 1989. Prior to the development of antivenom, 5% of reported bites resulted in fatalities. On the photo black widow (possibly Latrodectus mactans) - one of the most dangerous in the genus.
Source: Washington.edu, Wikipedia, AFPMB