The answer is yes and no. Yes, if you have a PSP-2000, PSP-3000 (aka PSP Slim or PSP Brite), or PSPgo. No, if you have a PSP-1000 (the original model).
Starting with the PSP-2000 model, Sony equipped the PlayStation Portable with video-out capabilities. Plugging a PSP into a TV--and you can use any TV that has the appropriate inputs, not just Sony HDTVs--requires a special cable that plugs into the PSP's headphone/microphone jack (on the PSP-2000 and -3000 models). Video-out cables can be purchased with one of three sets of plugs on the end that attaches to a TV: composite, component and S-video (Japan-only). The same cables will work for PSP-2000 and PSP-3000, but the PSPgo requires a special PSPgo cable.
There is no HDMI version of the cable, but considering the video quality the PSP is capable of playing, there wouldn't be any point. PSP movies do look surprisingly good on big screen TVs, though; I've plugged my PSP-2000 into a 42" flat screen to watch UMD movies and found the quality to be much better than cable television, and not too much worse than a DVD.
