1. Cheaper rates.
Europe has good post-summer tourism discounts like cheaper overnight rates, rental options, and it's a lower season for flight costs. The lowest season for flights is January to March, but who wants to travel then?!
2. Higher probability of good weather.
Fall can last a long time in Western Europe - and so can winter. Spring has a distinct chill to it, and sometimes it is still cold until June! Your best chances at enjoyable warmth and sunshine are during October.
3. Less traffic.
There is way less tourist traffic during autumn, both domestic and international, because most people don't travel in the fall. Everyone is just returning from their summer - and usually August - vacation time, getting back into the swing of normalcy.
4. Most colorful season.
Europe does a really good job of flowering up once summer hits, and those summer accents are usually kept up through October. Fall is the most colorful season with blue skies and and vibrant trees as the leaves change. There may not be any blossoming trees, but their lifespan is much shorter, and come with their own set of problems (see #5).
5. No spring allergies.
Once the many trees and flowers start to bloom in the springtime (anytime between March and May), your allergies will make you miserable, no matter how much fun you try to have. You might want to avoid springtime travel in general, anyway.
Fall is the best season for the combination of warmth and charm in the Northern Hemisphere, so you may as well spend some of those crisp, sunny days in Europe!
Next time you have the option to choose your vacation days: try them in September and October. I think you'll be pleasantly surprised and make fall your regular holiday time!