Is there a way to publicly raise Bitcoin funds? What services are available to publicly raise Bitcoin funds? 

I'm considering setting up a Bitcoin fund that would accept BTC donations. If the fund doesn't reach a certain value after a time, I'd like it to refund the BTC. Also, I'd like to give donors the option of withdrawing their donations once a week. It needs to be safe from hackers (eg. the BTC are stored on MtGox with Yubikey protection), and transparent.

Obviously I don't want to use a regular bitcoin wallet address as the public wouldn't trust it.

Does anything like this exist?
There is plans to implement conditional transactions which would do some of the things you indicated.   That hasn't been implemented yet.

To do what you want would require creating website from end.

For example you could display current balance &amp; goal as well as the number of donators.  When someone donates you could have them provide a "return address" (in case it is different) that can't be changed and a return password (which you encrypt).

While you said you want to use Mt. Gox I don't see how that would increase trust and it would make automating deposits and returns much more difficult.

In short it can be done but there is no easy automated way to do it within the Bitcoin protocol so you will have to custom build a lot of the functionality.