It depends on a few factors:
1) How much have I eaten that day? If I have an empty stomach, I can acheive a nice buzz on three 12 oz. beers. If you mean stumbling drunk, I cannot acheive this on beer, period.
2) How much did I drink the day before? If I put a few away the previous day, my tolerance will be up. It'll take between 4-5 in that case.
3) Is it draft beer, bottled, or canned? ANY draft beer gets you more intoxicated than store bought, even the 'lights'. I don't know why this is. And it seems that bottled beer always packs a bigger buzz than canned beer.
4) What brand is it? Most beers on the market are 5% alcohol. It doesn't really matter which brand of 5% you choose, one doesn't get me much drunker than the other under most circumstances (see #5). Then you move up (or down) into the 5.5, 5.9. and even 8.1% beers. If you're looking for a quicker buzz, go with one of these. Warning: these demand an acquired taste.
5) Is the beer my 'normal' brand or not? I've found that changing brands can bring on more of an initial buzz, even if they have the same alcohol content. I'm not sure why this is either. I speculate that I become accustomed to the recipe of my normal beer, and the new mix is a shock to my system. In conclusion, no beer (besides the 8.1 on a good day) can get me "drunk", and the number it would take to bring on a nice buzz is varies between 3 and 6.