I have an ASUS motherboard and it works just fine for me. I would buy another ASUS board in the future if the choice was between other boards of the same price and quality.
I can't speak for fully built ASUS computers, but it does sound pretty retarded if you can't open the case without voiding the warranty. Even DELL doesn't have problems letting you open the case and look inside. I haven't heard of any brands having such a strict policy before, but then again I don't know many people with computers from tiny OEMs either.
Every brand of parts has problems once in a while. I wouldn't say that ASUS does any more than any other brand. If anything they have a high raw number of failures because they are a Tier 1 manufacturer with a huge percentage of the market. If their failure rate is 1% and they sell 10 million boards then they will have 100,000 failures, whereas a no name brand like Zotac may fail 10% of the time but if it only sells 100,000 boards it will have 10x less failures than the example Asus figures.
It is hard to measure % good vs % bad since those figures aren't generally available to the average person, but I have been around a while and I haven't seen an abnormally large % of ASUS failing on these boards compared to other Tier 1 makers.
On websites like Amazon a happy customer is roughly 100x less likely to post a positive comment than a sad customer is likely to post a negative comment so you have to take these comments more as a list of possible problems and not draw any meaning for how likely the problems are to actually occur from them.
If ALL the reviews are bad, though, I would stay away.
I doubt it would be that way for ASUS boards though.
In any event, with competent handling there should be only very low failure rates with ASUS boards, like other major manufacturers.