Before my daughter was born I imagined that it would be fairly easy to keep on top of toys, provided I kept them well organized and easy to put away. My plan would have worked perfectly, too, except that I didn't account for an influx of toys that did not come from me! Toys are so cheap these days that it seems like every time you step into a shop or go to a restaurant you are handed some little plastic doodad, and if you kept every single toy you would never be able to walk across your living room again. Here's what has worked for me:
1) REPEL whenever possible: If you get a toy at a restaurant or some other place (and your child isn't absolutely enamored with it), leave it there for the next child. Remind yourself that the last thing you need is yet another cheesy toy that your child will probably never play with again.
2) EDIT when no one is looking: I like to take a minute or two during naptime or after bedtime and remove a few items that won't be missed. I usually put them in a bag in a closet just in case they are missed, and then I donate or toss the lot after I've collected a bag full. And for the record, my daughter has never once noticed the mysterious migration of toys into the closet.
3) GET KIDS INVOLVED if they are old enough: when s/he gets a great new toy from the grandparents, enlist your child to choose a toy to pass on to another child. For some kids this is easy, but others are more reluctant to let anything go. What has worked for me so far is explaining that there is no room for the new toy until she chooses an older one to "put away" in storage, but she is starting to get the idea that giving is not so much a loss for her as a gain for someone else. (How do you get your kids give up old toys?)
4) CONTAIN the chaos: set up an area that for toys that is as large as you think the toy collection should be, and once toys start to overflow you know it's time to get rid of some of them. I personally like the "color boxes" they sell in Japan because they are so cheap, durable, and fully customizable. Plus, you can get curtains, doors, or boxes to fit them perfectly so that when play time is over your eyes are not assaulted by shelves full of brightly colored toys. If you can't get something like this in your area, try a couple of bookshelves and install your own curtain rod on the top. It's cheap, and it's so easy for kids to put stuff away when they can see where everything goes. In any case, vertical storage beats the traditional toy box hands down!
Also, if you can get sturdy mesh bags, buy a hundred. As your kids get older and the toys come with more and more tiny pieces (Legos, doll clothes, etc.), keeping them under control becomes a real challenge. I use these sturdy nylon mesh bags (in gray so it's easy to see the contents), and my daughter happily puts all the pieces in the appropriate bag. OK, I admit she is a little bit compulsive that way, but I have heard other parents say it works for their kids too once they get used to the system. These bags are especially good because they retain their shape whether full or empty, so they're easy even for tiny fingers to deal with, and they are easy to organize in our bookshelf storage system.
5) ROTATE: Take a selection of excess toys and put them in an easily accessible (to you) storage area, such as a closet or garage. Then, once in a while, bring out the box and switch out the toys in the box for others in your normal toy area. Children are usually so excited by the "new" toys that they never notice that the others have gone on sabbatical. It's a pain to do this, but it may be worth it just to maintain your sanity.
6) WORK WITH THE GIFT GIVERS: People love to give presents to kids, and no matter what you say, it is pretty unlikely that anyone will easily give up that pleasure. However, you may want to casually mention several other things that bring joy to your child(ren) so that tangible gifts are not the only the only thing your child receives. Experiences like trips to the zoo, amusement park, aquarium, etc. make children just as excited, and they create memories that will probably last a lot longer than your average plastic trinket. Just giving a child your undivided attention for a few hours can be much more rewarding and make him/her feel more loved than even the most expensive toy. (It is especially nice if the gift giver has a personal talent or passion to share with the child, like cooking or fishing.)
What has worked for you?