What are the state of the art free natural language parsers?

If you're interested in constituents, I'd vote for the Berkeley parser, or the Charniak/Johnson one. I find the Berkeley parser to be somewhat more accurate on non-news text, but Charniak's is faster (use the -T50 option for a big speed gain with a minor loss in accuracy). They are both far more accurate than Stanford's. Even if you are interested in Stanford Dependencies, they can be extracted from the output of these others parsers, and will be more accurate than those produced by the stanford parser (see recent report).

For dependency parsing, I'd go for the MstParser (use the second-order model), or, if speed is important, my own EasyFirst dependency parser.

I think the Combinatory Categorial Grammar (CCG) are also well worth considering. The tools (can be found here) are very well supported and quite mature. As far as speed goes: I've heard they parsed all of english wikipedia with a few tens of machines in under 3 hours (but perhaps the experts can get the exact numbers).

Update: I can't find a reference to the wikipedia quote so it might be incorrect. In "Linguistically Motivated Large-Scale NLP with C&C and Boxer" I did find that they parsed the Gigaword corpus using 18 machines in under 5 days.

The Berkeley parser is very accurate (more institutional bias, probably), but I actually use the Stanford parser, which is far easier to use, better documented, and has accurate dependency parsing as well.

The accuracy varies depending on how close your text is to the PTB, but they've got F1's in the high 80's as far as I remember

Well, "best" how... Most comparative studies I have seen report Charniak's or Collin's parsers as most accurate. (Although Connexor, a commercial system, usually -- but not always -- scores materially higher.) However, in a comparison of dependency features, Stanford's parser usually wins.

Especially for biomedical text, there's Enju and Mogura which are HPSG parsers. They come packaged together, but Enju is optimized for accuracy and Mogura for speed.

There is also the Stanford Statistical Parser GPL with models for English, Chinese, German and Arabic and the OpenNLP maximum entropy based parser (English model only) under Apache and LGPL licenses. Both of them are implemented in Java.

In the python world the NLTK project comes with a bunch of parsers too.

I don't know whether they are state of the art though. I would be very interested in a comparative summary of their respective performances should someone here had tried some of them.

If you prefer to try a dependency parser (as opposed to a phrase structure parsers like the ones recommended before), MaltParser and MSTParser are good choices. Each of them has achieved state-of-the-art accuracy on several languages (which one is better for you depends on the language and dataset, of course).

Might be institutional bias, but I highly recommend the Berkeley Parser, which is state-of-the-art. I've found that its performance suffers a bit less from parsing non-newswire text relative to other parsers. Two small things: (1) it reports parse forest posteriors if you need them and (2) it is multi-core out of the box.

Update: I have a wrapper around the Berkeley Parser in my NLP Clojure package Mochi. See parser.clj.

Charniak's lab has released their parsers for a while, and those have always been state-of-the-art, or near to it. You should look at the relevant publications, but the self-trained parser is better than the reranking parser, IIRC. You can also use their self-training method to adapt their parser to your text domain, if you don't mind training it.

Besides that, for a while the parser by Carreras et al (2008, "TAG, Dy­nam­ic Pro­gram­ming, and the Per­cep­tron for Ef­fi­cient, Fea­ture-​rich Pars­ing") was state of the art. I emailed Terry Koo and asked nicely and he shared the code with me. Which just goes to show, it never hurts to ask.