The PlayStation 2 has been by far the most successful console of all time, surpassing its predecessor the PS1 by a large margin in sales, now to the tune of over 130 million worldwide. This is largely due to the consoles massive library of games, also the largest of any system ever released. With the increasing number of ways to download games off the internet, that library of nearly 2,000 games is entirely at your disposal.
While the average PS2 game is a rather robust 3-4 GB, computer technology has advanced a great deal since the aging PS2 was first released at the turn of the century, making download and storage of PS2 games easier than ever for users, and uploading and storing games on servers easier than ever for websites. For this reason, an increasing number of ROM sites are adding PS2 games to their collections, which would have been unfathomable even a few years ago. Even 700 MB CD-based games have only recently seen wide release on ROM sites, such as PS1 and Saturn games.
Because these ROM sites freely offer direct downloads of some PS2 games, they should be one of the first places you look. Just be aware of two key points at present. Firstly, only a handful of the most popular games are available at most ROM sites. Secondly, they may have downloading restrictions in place capping the amount you can download over a period of time, which would usually amount to no more than a game per day, much like similar restrictions you would find at other sites such as MegaUpload or Rapidshare.
Speaking of MU and RS, they are also viable options when it comes to downloading games, save for the above mentioned download restrictions (which can be waived for a monthly fee), and the fact that games get broken down into multiple parts due to file size limitations imposed by these sites (much smaller file size at RS, meaning the average 4 GB PS2 game comes in 40 parts). The trick is simply to find a site that hosts the link information to these files, usually found on gaming forums, as the game files are usually given random or chaotic names so as to avoid being taken down by the hosting sites, so they can not simply be searched for through the site itself.
Next, you can try one of the major direct download sites, which also require a monthly fee, but which feature faster downloading speeds, single file downloads, and large or even complete lists of games in one place. For the devout gamer looking to download PS2 games by the bucketful, this is definitely the most viable option.
Lastly is P2P file sharing, which is certainly a potentially option, though fraught with uncertainty. Firstly, as PS2 games become older and older, with less and less interest surrounding them, less people are sharing the files, making it difficult to find active files with even a single seed. Secondly, even if a file is found that is active, download speeds may not be all that good due to the limited number of uploaders. Lastly, there is a greater risk of encountering harmful files through this method than other.
There are many options when discussing how to download PS2 games. Depending on the amount of games you wish to download, as well as their general popularity, and the download speeds you wish to obtain, the option which is the best one for you will vary. Enjoy downloading some of the best games ever made.