PS3:Video Output Notes
It is generally best to use the PlayStation 3's HDMI output, however there are backward-compatible scenarios that make the PS3 an interesting tool.
The PlayStation 3 can output 480i, 480p, 720p, 1080i and 1080p from it is component video and HDMI outputs. The RGB signal will only output 480i and no other resolution. As a note, 240p is not supported from any output.
PlayStation 1 Video Output
Video quality is noticeably softer than when using PS1 or PS2 consoles. All PlayStation 1 games will either be outputted at 480i, or scaled to 480p and above. Generally speaking, PSN downloads of PS1 games look much sharper than playing original PS1 discs. As a result, the PS3 is a decent way to play PS1 games on a flat-screen TV, but a terrible way to try and play PS1 games on a CRT, unless you are specifically looking for 480p support.
PlayStation 2 Video Output
Decent video output. Some smoothing and filtering options are present that some people may enjoy.
PlayStation 3 on a CRT
The easiest way to play PS3 on a CRT is via component YPbPr video out. The PS3 is capable of 480i, 480p, 720p and 1080i over component YPbPr.
If you have an RGB monitor that supports 720p and HD SDi, you can use an HDMI to HD SDi converter to play games in the highest quality on your monitor. Most HDMI to HD-SDi converts are completely lag-free, as they only convert the signal between formats and do not use a framebuffer to change anything.