Game compatibility

PS3 games (on Blu-ray discs) are not region locked, but they are released and labelled with numerical regions codes (which seems to match DVD region codes).
Any PS3 game from any region will play in any PS3. However, there is the special situation when you try to play back the game in Standard Definition.
If the PS3 game only has Standard Definition and Enhanced Definition for either PAL (576i and 576p) or NTSC (480i and 480p), your PS3 must have the same Standard Definition and Enhanced Definition format support, or you won’t be able to play it. This is not a problem if you play the game in High Definition (720p, 1080i, 1080p), but there exists the possibility to region lock (based on Blu-ray game region) games if the publisher decides to do so. All PS3 games have a serial number containing a four character prefix, followed by a five digit suffix. The following are the common prefix for PS3 games:

The first letter indicates the storage format. Normally, it is B for Blu-ray disc format. Other formats may include S = DVD.
The second letter indicates if the game is first party (C = Sony), or licensed from third party (L = others). The third letter indicates: A=Asia, J=Japan, U=United States, or E=Europe. The last letter indicates the type: D = Demo, S = Game, M = ?.
Note that for some third party games, Sony may take it and repackage with appropriate material for other territories, thus the game become first party as well.

PS2 games are divided into four main regions (NTSC-J, NTSC-U/C, NTSC-C, PAL) and two formats (NTSC or PAL) locked. Note that the PS2 game discs can be single or double layer, although there are very few dual-layer PS2 games (like Metal Gear Solid 2 Substance). The PS3 supports both.

PS1 games (disc-based) are divided into three main region (NTSC-J, NTSC-US, PAL) and two formats (NTSC or PAL) locked. Most early PS (PSone) games are not protected, but later releases (like Metal Gear Solid Integral) have special marks that require special CD lens to read. The PS3 supports reading these protected discs. Note that PS games downloaded from the PlayStation Network store are not region nor format locked as long as you are able to pay (if not free) and download them from the store.

Movie compatibility

For Blu-ray video, the discs are divided into three (A, B, or C) main regions which must match the region of your PS3 for playback. The initial Blu-ray discs that were released supported region codes, but were not enforced, so a PS3 can play Blu-ray discs from any region (this might change in the future).

For DVD playback, the discs are divided into six (from 1 to 6; note 0, 7, and 8 are special cases) main regions and two formats (NTSC or PAL). Not only must your PS3 match the region, it must also support the format as well.

Compatibility Notes

Note that Blu-ray and DVD uses different region coding methods and country division, and they should not be confused with each other.
Also note that the above table only applies if you have the latest firmware version installed, which can remove or add format or region lock for DVD playback.
For example, the Hong Kong PS3 originally only played back NTSC Region 3 DVD, and with an update supported both NTSC and PAL Region 3 DVD playback.
Likewise, the European PAL PS3 gained the ability to play NTSC Region 2 DVDs (essentially Japanese DVDs). This indicates that the trend is for all PAL PS3 to be able to playback both DVD formats (NTSC and PAL discs in same region as PS3 or Region 0), whereas the NTSC PS3 (with the exception of the Hong Kong PS3) can only play the NTSC DVD format (all assuming same region, or disc with Region 0).
The situation is not 100% accurate, so provide feedback if you note otherwise.

As for model releases and dates, note that although the PS3 was not officially released in China, the majority of them are actually made there, so you can find all sorts of models in that country. The region codes for China designate what they should be if an official PS3 was released.

A long read here.