I see two main questions here:
- "Should I let my kids watch the older cartoons I grew up with?" (what you consider "quality cartoons")
- "Should I control what my kids watch?"
Personally, I see no problem with sharing the cartoons of your childhood with your children. I, too, watched Tom and Jerry as a kid. Through the 20/20 vision of hindsight, I see just how over-the-top the violence of that show is (much like another of my childhood favorites: The Three Stooges). However, when I saw that my daycare provider includes Tom & Jerry in her lineup of "acceptable" TV, I was more amused than concerned.
Violence in television has long been a hot topic for parents, but I personally don't find it to be a major concern.
Of more concern to me is the pace of the shows. Fast scene switches concern me more than cartoon violence (so far my son has not hit me over the head with a mallet).
So, in short, if you have fond memories of certain shows from your childhood, by all means share them with your children. Particularly if you do so by sitting down with them to watch the shows, and talk about how much you enjoyed them as a child, while reminiscing with them about other parts of your childhood (in other words, use it as an opportunity to interact with your children, rather than passively viewing the shows!).
As to controlling what your kids watch, I'd say "Yes!"... followed by the qualification "as much as you can, while you can". At some point (and this point varies depending upon your circumstances; primarily the amount of exposure your child has to other children) you simply won't be able to fully control their television habits. Whether it is that they are simply focused on being able to watch a show their friends are watching, or that they are watching television while you are not there to supervise, eventually they'll be watching content outside of your ability to control it.
Since the strongest risks associated with television viewing coincide with the earliest ages of development, the longer you can exert guidance over their viewing habits, the better.