What is the state of the art in summarization?

ROUGE is based on n-gram overlap between human and automatic summaries. Since good summaries can have radically different words, ROUGE has been (rightly) criticized as being pretty flawed. For example, Liu and Liu found poor correlation between ROUGE and human ratings of summarization quality.

That said, you're right that people still use ROUGE and compare against SOTA using it. The best place to look for current SOTA results is on the DUC data sets. (Haghighi and Vanderwende use DUC-2007 for evaluation.)

To address some of these problems Nenkova and Passoneau developed Pyramid scoring. Pyramid uses the presences of Summary Content Units (SCUs) to evaluate summary quality. SCUs are subsentential clauses that have some propositional content. One limitation of this method (and it's a big one) is that, to date, SCUs need to be manually annotated.

In summarization, the trend has turned toward abstractive summarization (including paraphrase generation, sentence simplification, natural language generation) from extractive summarization. Two major frustrations with extractive summarization was that 1) the summaries were constrained by the sentences in the source document, so summaries weren't especially good and 2) it was really hard to beat top-N sentence baselines (for news documents anyway). There's a nice paper by Carenini comparing abstractive to extractive approaches.

An excellent place to go for the most current methods is the Text Analysis Conference summarization track which took over from the Document Understanding Conference. Papers from 2008 and 2009 are available at http://www.nist.gov/tac/publications/index.html and the 2010 conference will take place this Fall. While the Haghighi and Vanderwende paper mentioned above presents what seems to be a very powerful method, it, like almost every system presented at TAC, is still a sentence extraction algorithm. Many approaches use a simplistic form of sentence compression where redundant information is removed or other information is compressed such that the main idea is still there, but it's still sentence extraction. Other methods that are in use include almost every machine learning algorithm out there, from the simple to the complex, yet the most simple is still extremely powerful and has been in use since the 1950's: simply using term frequency metrics. I'd be very interested in hearing what other people are up to as this is my graduate research area. I'm currently looking into similar approaches to H&V using topic models and other generative document models to learn the most salient sentences in a corpus.

An interesting and rather straightforward way to select sentences based on semantics was proposed in this paper that used latent semantic analysis for summarization. There also exist simple variants of this that can be applied for multi-document summarization and update summarization as well (see this paper).

Perhaps not state of the art, but a simple and easy to understand approach that serves as a good starting point and a very reasonable baseline to compare to other techniques (and produces very reasonable results) is H.P. Luhn's approach in "The Automatic Creation of Literature Abstracts" dating back 50+ years. It's along the lines that Will Darling mentioned in an early comment: you basically find important sentences based upon a simple form of feature detection that takes into account distances between the most frequent words. You can find the original paper online, or you can check out an implementation of the algorithm that's presented in Mining the Social Web from its GitHub repository.