I have a 2 year old desktop. I concur with about 1 crash per 40 hours--just involves going back to the last autosave.
Have had no performance issues: AMD 64 x 2, 3800+ 2 GHz, 2.0 GB Ram. Smooth as silk performance--though I am almost always at the slowest setting.
Despite it quirks, I consider HOI3 brilliant.
Want a possible whacky history? Start at 1936.
Want more realistic history? Start 1939 or later. [This is to answer the compliants on one side or another]
Want human controlled Italy, for example, to be a superpower? Fine. Don't want that to be possible, because it is so ahistorical? Great--crank up the difficulty, or set yourself rules. [ie--don't exploit AI/game weaknesses, or pre-knowledge. For example, can Italy invade successfully Yug early against the AI? Pretend it doesn't matter, and don't do it, because it would have been such a huge risk in real life]
Want more challenge? Never go back to a previous save when something does not work out. It invalidates the FOW and Intelligence element to "try something out," or to neutralize a freak battle. Oh...you want just have a relaxing time, and crush everthing in your wake...then, by all means, try things and go back to previous saves if they do not work.
The supply management? I consider it brilliant, though you will hear much moaning in this forum about it. Appropriately boundries the human players capabilities, and the complex interactions with infrastructure and convoys seems generally historical.
The HQs? Again, I like them. Maybe burdensome for the large powers, but the Corps structure seems great for a smaller power. I like fiddling with the OOB--again, there will be significant dissent about that in this forum, but it appears you can ignore the HQs if you wish--making the whole system very flexible.
And the 1.4 patch is likely to make things even better. Yes, there is the superstack issue, and naval warfare needs a CV-sensible redo. Glass 9/10ths full?