The A8 is a quad core too which may help in certain things. All in all though the i3 will normally outperform it in terms of CPU power and also consume less power. The main reason for the A8 is the graphics.
You're correct, the A8 is usually used in HTPCs where a big discrete graphics card would not be needed, but a graphics card would help in the video playback. If you really want a gaming PC, then the i3 2100 is way better than the A8. As for jmsellers' comment on it being 4 cores, you can easily buy either the Phenom II x4 960T or the FX-4100 for generally a cheaper price than the A8 and still get the 4 core performance. Another downside to the APUs is that it uses a new motherboard socket type: FM1, which isn't really common.
Possible as it depends on the discrete GPU. IE any card upto the 6670 will crossfire with the A8-3850. Graphics wise you end up with about a 6730. Any larger tho I would suggest an i5 2400. I don't like suggesting the i3 as they tend to have higher latency. OS network processing must compete with FPS push for CPU cycles. Quad cores with under used cores tend to see less FPS loss and or lower latency. Another advantage with an i5 is the other programs you run will have less of an effect on FPS. Programs like VOIP, antivirus, and software firewall can all still away FPS on dual cores to a much greater degree than quads.
If you must go intel dual core I suggest the G860 as its about the same performance as the i3 but lower priced. Note the green bar is average being about .8FPS higher. The G850 maybe the best bang for the buck and price wise you can buy a comparable GPU to A8's.
it is interesting as a cpu though because if you use the right gpu you can really boost the graphics processing power, basicly crossfire, with the cpu and gpu. the cpu graphics are supposed to boost the discreet gpu about 70%. that is a lot of power with only buying cpu and low end gpu, essentially giving you a beefier gpu for price of lower end gpu and a cpu which you could spend same amount of money on with alternatives.