A magazine just asked me to provide them with a brief exposition of my views on the main sorts of wine bottle stoppers currently available, and since this continues to be such a hot topic, I thought I would share it with you.
Natural corks have the advantage of having proved themselves able to encourage the subtle evolution of top-quality wines for decades and are both biodegradable and part of a historic ecosystem in southern Portugal BUT a) they're a pain to extract (you need strength and a special implement) and b) perhaps more importantly, a substantial proportion of them fatally taint the wine.
Screwcaps have the huge advantage of being extremely easy to open and re-seal (no special equipment needed) and keeping the wine as clean and fresh as it was when the winemaker put it in the bottle. The only disadvantage of screwcaps is that some people are prejudiced against them and they have not yet proved themselves a perfect stopper for very long term ageing of top-quality red wines (which may need tiny quantities of oxygen, allowed in by natural corks but not so far by the screwcaps on the market).
Synthetic (plastic) corks have the great disadvantages of being non-biodegradable, not especially easy to extract and, often, impossible to re-insert in the bottleneck. They are free of the taint problem but research so far suggests that they provide an effective seal for only a year or two, so are only any use for inexpensive wine. They also require a corkscrew and are no less expensive than natural cork.