Internationally speaking (since I'm not in the US) I think the summer will be topped by:
Pirates 3
Harry Potter 5
Spiderman 3
Shrek 3

with quite a bit further down:
Bourne 3
Ocean's 13

"Pirates" is easily going to win this battle.

Yes - Bourne is the adult fare - Ocean's is questionable - it better have great reviews - but I do think Pirates will win

I think Spiderman will probably prevail domestically, whereas Pirates will win internationally.

I am hopeful for Ocean's though-- the second one was somewhat of a disappointment (understatement), but I do love the first

I too favor Pirates as the BO winner. The Rings trilogy increased its box office takings with each successive instalment. It similarly was one long story rather than 3 standalone films. Pirates was huge second time around despite mixed reviews. Why wouldn't this same audience want to see the story concluded? Especially in light of a trailer promising much of the same humour, action, and well crafted and integrated special FX. And it belonging to a genre best seen on a big screen with big sound.

I agree, I think Spidey wins domestically, Pirates is second (but doesn't top 400). and Shrek doesn't get to 300 (but Potter does).

I agree the marketing has been brilliant and effective for Spiderman, it gets a two week headstart, and one only has to see the weekend returns to see that EVERYONE is passing on the week's lame releases to see Spiderman this weekend. 130 million 3 day and a second weekend of 80-90. Pirates, I think will only get to 130 with the four day weekend, and won't be able to makeup the difference because it'll be competing with Spidey and Shrek (and eventually Evan, Transformers and Potter), something Spidey won't have to do until it's fourth week. Shrek is unfortunately stuck in the middle, and hasn't had very good advertising. Pirates still hasn't come up with a campaign as successful as "Pirates! Pirates! Pirates! Pirates!..." from last year, and I think the marketing should have started earlier to let people know the third one was coming in less than a year, rather than two, three or four years down the road, like probably 95% of the Pirategoing public thought last year.

Worldwide Potter or Pirates probably take the cake.

Just to add:

I saw Pirates last night (in Belgium it hit screens May first at 12:01 am) in a packed cinema! There must have been 10 screenings during the day and from what I heard all sold out (or close). SO yeah, big money for SPidey!

Unless word of mouth dissuades people from going later on... because personally I found it a bit disappointing! (story-wise) It felt spread too-thin... But liked the ending! ;o)