Apples share price may reach $1600 in 3 years according to analysts. Apple's present share price is around $670.

This would make Apple worth more than many countries!

Personally I doubt it but with heard mentality of their followers who knows.

http://m.cnbc.com//id/49008812

That's the thing. the share price is almost independent of what they do as a company.
People want to buy Apple shares because they keep increasing in value and they keep increasing in value because people want to buy them.

All Apple need to do is not screw things up (ie stay profitable - not hugely difficult when people will buy stuff based solely on your brand name) and the share price will take care of itself.

Not true. Probably 95% of Apple stock is bought by hard nosed investment fund managers, who are looking at the underlying business fundamentals as well as future issues. Apple's stock price reflects a relatively modest P/E ratio, nothing like the ridiculous valuations of the dotcom era.