I searched around on the net and found that a typical 11 inch diameter helium balloon can generate 4.8 grams of lift. So then taking a weight of 165 lbs and converting to grams, you get 74,842.741 grams (according to google conversions and calculator). So by taking that number and dividing by 4.8 grams, you get 15,592.237708333333. So based on this, I would say that it would take about 15,593 balloons, because that's the number of balloons it would take to lift that amount of weight (assuming 11 inch diameter balloons filled with helium). Now it might be slightly less or slightly more, but from what little I know about hanging... However because I'm weird I just decided to look up how much weight it takes to actually kill someone with hanging...
After looking around I found that it takes 40-50 lbs. (18,143.6948-22,679.6185 grams) of pressure on a person's throat to choke them, causing death. So assuming that 40-50 lbs. (18,143.6948-22,679.6185 grams) of lift, provided by helium balloons would be enough to choke you, then you'd need between, 3,780 (3,779.93642) and 4,725 (4,724.92052) balloons (assuming 11 inch diameter filled with helium) to hang someone weighing 165 lbs. with an average size/strength neck, and kill them.

I'm weird I know... That and I'm messing around on Yahoo! Answers....

also, just because I can, here's what I put for "sources":

http://www.cockeyed.com/science/hel.....m/helium.shtml
http://www.google.com/search?aq=f&a.....5+lbs+in+grams
http://www.capitalpunishmentuk.org/hanging2.html
http://www.google.com/search?hl=en&.....=&gs_rfai=
http://www.google.com/search?hl=en&.....=&gs_rfai=
http://www.google.com/search?hl=en&.....=&gs_rfai=
http://www.google.com/search?hl=en&.....=&gs_rfai=
(I didn't use google to calculate the 74,842.741/4.8 grams.... I used the little calculator that comes already installed on PCs)