There's an interesting discussion going on over at Isis's palace regarding the personal statement essays required by many REU sites as part of an application. I run such a site. Following are some thoughts on how (and perhaps how not) to apply to REU sites.
A summer spent at an REU site can be a wonderful experience that can help you decide whether a career in scientific research is for you. Or a career in science in general. That's what the REU program is all about. It's not for padding your CV. Only apply if you're serious about working through the Summer. Working hard. At the end you will have learned a lot. And maybe earned a stellar reference letter or two that will help get you into grad school or where-ever you want to be next.
Keep in mind these sites get a lot of very good applications. It's very competitive. Here the acceptance rate is below 10%.
Choice of Sites
There are oh so many sites to choose from. Choose carefully. Don't spam them with applications. We can see right through that kind of thing.
Apply only to those sites you are truly interested in. And have the background for. Majoring in mediaeval music probably won't be seen as a big plus at that physics site you've applied to.
And don't think you need to attend a site at an Ivy league school. I'm at a state school. Former participants from the site I run have ended up grad students at some of the best schools in the country.
First, you MUST be a U.S. citizen or permanent resident. That's an NSF rule. Can't be bent or broken. Don't bother applying just because you have work authorization. It's not enough. If you're not a citizen you need a green card. Nothing else will do.
Have a decent GPA. I'm afraid anything under 3.0 just isn't looked at. If you're below 3.2 you need a really good explanation for why this doesn't reflect your true potential. We get a lot of applications with GPA's greater than 3.8. It's very, very competitive.
That pesky personal statement essay thingy needs to be good. Truth is, if everything else is stellar you might get away with a poor essay. But by stellar I mean so good every site you apply to calls to offer you a slot with double the stipend of everyone else. Plus accommodations in a five star hotel. That good. You're best bet here is to a) avoid the long list of relatives who have died of assorted diseases you wish to cure, b) avoid the cutsey story about falling in love with the chemistry set you got on your third birthday, and c) tailor your letter to the site you're applying to. Tell us why you want to spend your summer HERE. And read Isis's advice.
Prior research experience. Had a whole bunch? Great! Good for you. Too bad we probably won't take you. The REU program is aimed at giving research experiences to students who have few, if any, opportunities to do research. A little prior research experience is okay. A lot means you might not get an offer. Not all sites conform to this approach, but I have been assured by other REU PI's that not doing so can have serious consequences for the site. For example, not getting the grant that supports it renewed...
And then there are the...
Letters of Recommendation
I cannot overemphasize the importance of your letters of recommendation. These can easily make or break your application. They need to be good. They need to be sent on time (this year I received one a month to the day after the deadline - way after we had sent out offers). They need to be good (did I say that already?). They need to be substantial - two sentences saying you're the best student since the last one they wrote a letter for won't cut it. And they need to be from people who can really say something about your potential in science. Not from relatives (yes, had one of those... Mom was very proud of her little boy). Not from your favorite English professor (I've received many - they're mostly useless*). Not from the manager of the store you've been working in part-time (okay, those are a bit better than useless, but still not great). You will be accepted into an REU site based on your scientific potential. That is what these letters must address. And most of all, they need to be good.
[Update] How We Choose
I forgot to talk about this bit. It's kind of important.
So given the above, how do we choose which applicants to make offers to? I can't speak for other REU sites, but here we try to take a balanced approach. Setting aside criteria like belonging to an under-represented group (a big deal for the NSF), our perfect candidate would be the following: someone with a 4.0 GPA, from a small college, no research experience, professing a unquenchable desire to attend grad school, with stellar letters of recommendation.
We've only ever had a few applicants like that (we've had many come very close). So how do we choose? Well, someone with a 3.8 GPA from a small college would be ranked higher than a 4.0 from an R1 institution (plenty of potential research opportunities). High grades in science courses are more important than high grades in non-science courses. Stellar recommendation letters will trump GPA's to a point. Lack of research opportunities will also trump GPA's to a point. A clearly expressed desire to pursue a scientific career (research or otherwise) ranks high. In the end, it's somewhat subjective. It has to be.
Contacting the Site
It is perfectly okay to contact the REU site you've applied to to make sure all your materials have arrived. Or to find out where they are in the sorting/ranking/making offers process. It is not alright to have someone else contact the site on your behalf. Especially not your Mom. Trust me, that leaves a very, very bad impression.
Declining an Offer
Finally, let's say you're one of the chosen few and receive an offer from one or more REU sites. But you've already committed to another site (or internship). Please, please, please don't wait to decline. As noted by FSP recently, too many (i.e. more than zero) students leave declinations until the last minute, or worse, "forget" to decline offers. If you do this you may well be screwing another student. Someone who really, really wanted to get into site A, but had to accept an offer from their second or third or fourth choice because the acceptance deadline arrived before they received an offer from site A. Even if you're not screwing someone else (and you'll never know if you did), it's just plain common courtesy.
* The letters, not the English professors.