Snickersnack: I've been researching this for my PS2 and PSP the past couple of days. The PS2 is actually rather difficult. Most of its games are output to 480i. A simple component to hdmi or vga transcoder will not do. It's needs a deinterlacer.
With regards to the PSP, the HD Box Pro is one solution (is that thing really safe?), but if your PSP is modded, you can use RemoteJoy to output your PSP video via USB to your PC.
SirPrimalform: Apparently one of the differences between HDMI and DVI is that HDMI lacks the analogue signals, which is the only reason DVI to VGA adaptors can exist. In other words HDMI to VGA is not simple.
Fair point. You can do HDMI to DVI, and you can do DVI to VGA. I have a VGA/DVI adapter lying around somewhere, and my PC gaming TV has a VGA socket (funnily enough though, my monitor doesn't!), so I may have a play around later and see what happens.