Lets say you have a video file with the following data
Picture:
1920x1080
H.264
30fps
8000kbps
Audio:
48kHz
AAC
160kbps
2 channel stereo
and you want to watch it on your shiny new 40 inch LCD TV connected to your computer over HDMI. My current laptop can't play h.264 videos at anything more than 1280x720 without skipping. ANY NEW computer you can buy today will have no problems playing that video. I would say a system with
Core 2 Duo E series
2GB RAM
Radeon 2xxx series (except 2900) or GeForce 8xxx series
should have no problems playing that video either. Those GPU's are anything with UVD or Purevideo or any newer revision of those two. That system is probably a bit much to be called "minimum" too. It shouldn't have a problem with Blu-ray disc content.
EDIT: My laptop can play 1920x1080 h.264 videos. My desktop cannot without skipping
So that Core 2 system I mentioned earlier is a bit much. If this laptop had a BD drive it could do blu-ray as well. I played a video over HDMI to a 32 inch LCD TV to test the laptop.
You'll need at least a 2GHz+ dual-core processor (Core 2 Duo, Athlon II, Core i3, etc), and a dedicated video card that is either: an nVidia GeForce 8/9000/2/4/500 series, or an ATI/AMD Radeon HD 2/3/4/5/6000 series.
Basically, that means any desktop or laptop that has been sold new for $650 or more in the last four years. If you want a new desktop with those specs, you could get one for $500. If you want a laptop, you'll have to be careful that you get one with dedicated graphics. The newest Intel SB integrated graphics are okay, but if you go with that, make sure it has Intel HD Graphics 3000.
You could get a Blu-ray drive too...if you buy porn on Blu-ray. I don't imagine many people do, though.
Any computer that has an i3 processor or better, mostly because if it has a modern processor, and chances are that it probably has a modern graphics card too.
A pc with a decent(not totally crap) Nvidia that has cuda like 9500gt(which i have) and i guess whatever cpu is more than enough since only 10-20% of my amd 5000+ is used when playing 1080p videos... but this is valid only for 1080p videos which are not encoded in 10bit cause they need definitely something like an intel core2duo e series at 2.6ghz... but as far as i know there aren't really any hentai videos that are 10bit and 1080p - only 720p 10bit which require a less powerful cpu.
Anything with Core2Duo above 2.4Ghz is capable of watching HD movies
But I could run 1080p movies fine with a 2.0Ghz Pentium and Nvidia G103M (my laptop)