When planning a trip to Europe, something to keep in mind is when the crowds are out and about. One of the best ways to save money is to steer clear of high season. Different regions in Europe have different high seasons sometimes so you want to be aware of that before you start planning a trip to Paris in August.
June and July tend to be the most popular times to visit Europe. However, in some parts, like where the weather is very hot along the Mediterranean, "low season" is really when everyone is clamoring for some sun because it's waning back where they are from so be weary of places like this! Also, Paris's high season happens to be August and not July, along with the springtime. However, be careful with low low seasons because that is when some cities shut down all together or severely cut back hours (such as in Rome).
From mid November until Easter, excluding Christmas and New Years, most parts of Europe are not enjoying hoards of tourists. However, this is because it's winter and it's very cold in some parts. Be aware of this; but if you are brave enough to travel during this time, not only will you enjoy low season, you might just discover a side of Europe you hadn't dreamed of finding.
You'll find shoulder season, the time between low and high season when the weather is travel friendly and the sites are less crowded, generally between Easter and June and late September to mid November. Although these are great times to travel and many people won't be traveling at that time, these times get increasingly popular as the secret of shoulder season has spread.