You can't see all their holdings. But you can see quite a bit.
Section 13(f) of the Securities Exchange Act of 1934 requires all institutional fund managers with more than $100 million in assets to report their holdings each quarter to the SEC *(within 45 days of the end of the quarter). The hard copies of these filings go back 30 years, but they've been available for free online through the SEC's EDGAR database since 1999. The form name is (not surprisingly) "13F" or "13F-HR". Like many academics, I've used the electronic database of 13F filings put out by Thomson Financial (which has information back to the early 80s on electronic media, runs 5-10 gigabytes, and requires you to have some programming chops to access) in my research. But you can access a fund's data one filing at a time through the Edgar site.
It won't show things like derivatives holdings (at least usually not) or short sales. But if will give you an interesting look at the holding of the big boys. However, you might be looking at a portfolio as much as 45 days old. So, it's best for funds with a long-term (usually value-oriented) approach. As one example, here's the latest filing from Seth Klarman's Baupost Group.
And in case you're interested, here's one for Bernard L. Madoff Investment Securities LLC (I hear the founder has been in the news lately).
HT: World Beta who uses this information in an investment screening tool.