But this one doesn't have all the documents. There's a free system called PACER which allows you to download the filings for any federal court case, but it costs about 10c/page (although you can get a certain # free every quarter). As you can see form the link above, litigation generates a lot of paperwork so if you're interested in a case you can easily run up a large bill on PACER. Usually people who are interested in litigation share key documents from a case because court filings are by definition in the public domain. But this is slow and unreliable and if you're a law nerd the minor procedural filings are often as interesting as the important documents like the complaint or key motions.
The reason for the 10c/page PACER fee is to support the digital infrastructure required to provide it; Congress controls the budget for the federal courts an is notoriously stingy - perhaps because many members of Congress are unenthusiastic about funding another branch of government that has the power to strike down legislation - see for an overview of the funding picture http://www.americanbar.org/advocacy/governmental_legislative...
State courts are a whole different ball of wax. Some have everything online, others don't.
One other thing to be aware of is that if you're interested in a particular case and you want to know what happened at trial - with all the exciting (?) cross-examination and 'Objection! overruled,' moments the court transcript is not an official court document. The court reporters who produce them are hired by the attorneys and they charge a small fortune for copies. Now, because the trial is public domain the transcripts are almost certainly in the public domain too (this is law in the 10th circuit and I don't think it has been contested elsewhere). So if you can find a copy of the transcript on PACER* or one of the parties' websites, you're likely free to use it. The court doesn't hire reporters because they charge a lot - it's a very skilled job that's not so easy to automate as you might think - and the transcript only has legal value in the event of an appeal, whose benefit would accrue to one or other of the parties rather than the court itself.
Some courts have audio recordings of the trial available for free or relatively cheap, and many appeals courts, including the US Supreme Court, have recordings of oral arguments that are available for free. As data storage becomes increasingly cheap then full audio copies of trial proceedings will probably become the norm, but if you are listening to one then you'll quickly realize why court reporters charge so much.
* You probably won't find it on PACER because appellate courts generally don't want or need to see the entire trial record, but sometimes you can. Be careful if you do, transcripts often run for hundreds of pages and you'll be billed accordingly.
