There have been three periods of demos. The 90s through the early 2000s were the era of the free demo. Every game had one, and they begged people to try them out as a way to introduce their new game to the public.
The mid 2000s saw the worst trend - demos used as incentives. This period saw companies offering access to demos as incentives to pre-order, as rewards for registering and so on. Instead of them trying to get us to play their demos, they actually had gamers essentially paying to be advertised to.
The last four or five years, though, has seen the demise of the demo. They are the exception rather than the rule, unless you're talking indie. For mainstream titles it is more remarkable when there IS a demo than when there isn't. 'No demo' is the default answer these days.