Your question can only be answered on a case by case basis, and is heavily dependent on your personal taste. Some cars are "classics" even when they're new, some cars will never be more than old jalopies. In some cases newer vehicles benefit from the classic status of their older series brethren, like the 240 series and VW beetle.

As for insurance and taxation purposes, it depends on your national or state legislation. Here in .nl cars are considered classics for tax purposes (free road tax!) when they're 25, some insurances use 25 as a cutoff too but quite a few are happy to take 15 or 20 year old cars as classics provided there's some link to them being treasured as a classic rather than a cheap banger (such as being a secondary car, club mecbership, ...). Due to the rather hefty road tax the value does indeed increase as the car approaches and passes the 25 year boundary. .uk has a cutoff of "before 1973" if I remember correctly.

Bram