- The first site I'd recommend is Chessbase:
This site has a massive searchable database containing over 8 million games, including very recent matches, meaning at the time of this post 2016. The interface is very well designed and feature rich (such as presenting per move statistics). The site's authors do a reasonably good job of establishing comprehensive sets by pursing all extant copies of a particular player or tournament.
Although this database is essential, the site's features favour those who log in. The basic account is free, and it's credentials are accepted at sister sites, however to getting PGN of particulars game you need a premium account.
- The second, more historical site to check out is ChessGames:
This site's vast database of historical chess games has over 812,000 games, all searchable via the sites Search feature. Many of the not-so-recent historical games can be found in this gem-of-a-site. That said, the games are accessible in PGN format one at a time.
- The third site to checkout, more specialized, is 365Chess:
Many players have seen as high-profile sponsors of top calibre competitions, or great match GM commentators. Accounts are free to create, and the site has other useful features such as the "Chess Opening Explorer" which allows you to create notes for particular openings (useful for study).
Also, the site presents a subset database of openings by players of 2400 ELO or more. The games included in the Masters Database are also part of the Big Database, but if you search or browse the database you'll obtain only games of the most talented masters. This database is called "The Masters Database".
Another really nice feature is the ability to download all games by a particular player, but this feature requires a full membership, so not available to the free hobbyist.
- The fourth site to check out is PGN Mentor:
This site freely gives away complete sets of PGN games for specific players. They download as .zip files. Likewise, the site gives you the ability to download compilations of games categorized by opening. The sets you get aren't entirely current, and the sets not always complete (meaning important games for examples are left out), however they are free and generally pretty good. That makes this site invaluable!
- Finally, check out Mark Weeks collection:
This is another recommended site with surprising curiosities such as Kasparov vs. IBM's Deep Blue and very early (historical) games. The site is not fancy looking but nicely organized grouping by "Pre-FIDE" and "FIDE". It claims to have millions of games, but honestly, I haven't yet given this site the attention it merits to get a sense of this.
- A recommendation that came from a read is This Week In Chess
This site keeps you up to date by delivering you Weekly updates, specifically, daily Chess news and games are in this weekly digest for download, by Mark Crowther. The site says "Every Monday The Week in Chess covers all the latest news and games from international chess. Download the zipped file of games in PGN or ChessBase (cbv is the modern format) format for reading off-line."
If you have other recommendations and 'must have' sites that provide PGN resources, please