The Simpsons has been running since 1989, and now has 760 episodes in 35 seasons. The prime time animated series always had gags for adults and children, who appreciated different parts of the show. If you are too young to have seen the earliest episodes, you've probably been able to catch them in reruns. There are plenty of jokes you may have missed the first time around because 1. you were too young to get the joke, or 2. the gag may have relied on much older cultural references that you never encountered, and there were also 3. some jokes that relied heavily on current events, which were no longer current when you caught the episode years later.
In looking through the 13 joke explanations at Cracked, some were always funny to me because I was an adult when the series premiered and I knew the cultural references. Some are just too subtle and may have only gotten a laugh from the production crew. And a few were only funny for that one week 20-something years ago, and only then if you were up on the news. Check them out and see how many you recall.
Today I learned the "Ich bin ein Berliner" definite article use, implying a jelly doughnut instead of someone from Berlin, is a false urban legend.