Gooserider explained it pretty well in response to the question of intermittent loads. One key additional point - at every instant in time, the amount of power generated is equal to the amount consumed - excess doesn't go anywhere to be stored (with very few pumped power storage systems as the exceptions). So the utility is constantly monitoring usage and adjusting generation output, or raising/lowering voltage, to account for shifts in demand. Since there are a lot of people using power, dips and peaks in demand tend to average out pretty well, and usage usually increases or decreases in predictable ways at certain times of the day.
So, imagine that you are the guy who is in charge of making sure that there is always the exact correct amount of electricity generated at any given moment in time. Well, for you, predictability is the most important thing. You want to know that you have a huge amount of base load generation (read coal and nuclear power plants) that just cranks away at 100% output 24/7 - these plants take hours to bring on-line and can't be turned on with short notice. Then, you want some additional generating capacity that can be added quickly as needs change - things like hydro or natural gas fired generators. These can be brought up in minutes. Your backup is to bring power in on high voltage transmission lines to fill any gaps. The whole mentality of the power utilities is built around thinking like this, and renewables link wind (when the wind blows it blows) or solar (their worst nightmare - clouds cover the solar arrays) cause problems in large numbers. If the wind generators and solar arrays are just 1% of the capacity, then no big deal - it's in the "noise" to them - but when it gets very large, it causes real problems with the system they have set up.
Enter the "Smart Grid" - instead of blithely ignoring demand and trying to match generation with demand instantaneously, you manage the demand when it spikes. Or take advantage of excess power when it happens to be available. If you have an electric hot water storage tank, there are a lot of options as to when it gets heated. It can get turned off when generation capacity is tight, or turned on when there is excess power to be "soaked up" (i.e. the wind is blowing really well on a sunny day). The problem is that you, as an electricity consumer, have no incentive to care about this at all - you pay a flat rate regardless of time of use. If the utility knew when excess power was available, told you (or your appliances) that they could get a great rate on this excess power, then it could get used when it was available, and the ability of the grid to consist of more renewables would be greatly increased. Greatly increased, but not to 100% renewables - you still need some base load generation that can always be counted on UNLESS you accept that your power will be shut off at random times with no recourse (probably ok in the third world, but not in the US) when the wind isn't blowing, the sun isn't shining, etc. Or, instead of having the base load generation, we can just string thousands and thousands of miles of high capacity high voltage transmission lines to connect the East Coast with North Dakota and New Mexico or whatever and take advantage of their wind, or the sun in New Mexico, or whatever. Problem is, these cost $1 billion per 100 miles - not very cost effective. Much more cost effective is to have some base load generation near to where you live. Most people complain about their electric rates now - imagine if they doubled or tripled - that's what would happen if you try to go 100% renewable. But 60% renewable is possible without breaking the bank provided you have a Smart Grid.
Look at Denmark if you want to see the “hazards” of connecting turbines to the grid. They seem to be doing this very well.
True - Denmark has huge wind capacity, and on paper they generate much more than 20% of their power with wind. They also have one of the most extensive high voltage transmission line grids in the world that they use to export their wind power when they can't use it all. Other countries nearby benefit from this, but if every country did this, it would be difficult if not impossible for everyone to have this much wind generation capacity. There are some practical limits. I wish there were not, but there are.