The Celeron G530 will play 1080p. Although the G530 is no rocket, it has an IGP to decode blueray and its CPU core's general computing power is still multiple times faster than the fastest P4. I don't think there is a modern desktop CPU from AMD or Intel that cannot play 1080p. Just don't pair it up with P67 mobo or you won't get video out for IGP (I don't expect you to get P67 if you are on a small budget thou).
HTPC use is the what the G620 is best at. The CPU cores aren't fast enough for "real CPU tasks", and the IGP isn't good enough for 1080 gaming. It is good enough for most of the HTPC duties however, and has a low TDP making it a good choice.
you get no widi, 3d stuff, clear video, quick sync with pentium or celeron. may be that's why intel doesn't call celeron/pentium's igp only hd graphics, not hd 2000.
a pentium g860 + h61 mini itx + 2x 2gb ram + radeon hd 6450/6570 would make a good htpc/ budget pc. although, a quad core llano would make an even better htpc.
I use the G620 in my HTPC, although I offload the video duties to a discrete GPU. The CPU is fine for what I use it for though. The system can be a bit slow occasionally but no issues with HD playback (Bluray).
It depends upon what types of video that you watch.
Don't hold me to this, but I think the P-G620 uses the "Intel HD Graphics" of the 1st gen Clarkdales - it should work but you will see high cpu utilization without any post-processing.
And again, just an old guy with a long memory, here, but I think the HW acceleration would be fairly limited and may possibly require third-party software decoders to function correctly.
It will handle your typical mpg2, h264, BluRay, and a dead vc1 ... but probably limited or no HW acceleration for flv, xvid, divx. It's somewhat like the AMD UVD on the HD5450 but probably with limited video acceleration for some formats and resolutions.
You should also check for Silverlight acceleration if you do Netflix. Snagging an HD6450/5450 might not be a bad option if you have issues.