I have planned our weekly menu on and off since we got married, but lately I have been really working hard to stick with it and it truly makes a difference in our grocery budget. To make planning easier, I have created a list of about 35-40 meals that we like to eat, and I just rotate those meals in and out during the month (I do try out new recipes fairly often, but its nice to have a basic list of meal ideas that I can always fall back on).
I plan the meals one week at a time (sometimes I'll do two weeks in advance, but I'm not always as good at that), then create my shopping list. I always make sure to have a good supply of stock items, such as milk, flour, eggs, sugar, tomato sauce, spices, pasta, etc, so most of my weekly list items are meal specific. I get everything I will need for the full seven days (or two weeks) and only go to the grocery store again if I forgot something essential (which is rare). I have become a much more creative cook and am often substituting items in and out of our meals so that I don't have to go to the store again.
Menu planning saves us money in lots of ways. First, making our list keeps us from wasting money at the grocery store by buying items at random, or buying more than we need. Also, have you ever noticed that you go to the grocery store for one thing you end up buying five things? Getting everything we need for the whole week in one trip keeps us from buying those extra things when we meant to only get one. Menu planning especially keeps us from being tempted to eat out, which often is a result when you come home hungry and don't know what you have or what to make. It is also healthier because we make almost everything from scratch.
I know I'm not the first person to plan out meals in advance, but I also know that most people don't do this. If you are looking to save money, this is a great way to start.