They have so many classes and rankings now that they've given up even trying to use the word "class" anymore.
At the top you have Jehovah God, who is nominally in charge of EVERYthing but doesn't actually DO ANYthing.
Second, you have The Now Reigning King, Jesus Christ, who like Jehovah, is also nominally in charge but doesn't actually DO ANYthing.
Then, you have those of the 144,000 anointed who have already died and been resurrected to heaven to rule as kings and priests for 1,000 years. Like their brother Jesus and dad Jehovah, these also do NOT do ANYthing at present.
Then you have your legal officers and attorneys for the Watchtower Bible and Tract Society. This is the first group that actually does anything as you head down the corporate er, Kingdom ladder. These guys tell the Governing Body what to tell the rank and file JWs what to do.
Next you have your Governing Body. These seven men sort of do things. Every Wednesday morning they meet for a couple hours to talk about the work their committees are doing and decide that the status quo is treating them all pretty well. If they feel saucy, they may discuss some new light to spring on the rank and file later in the year and commission someone in the Service Department to have it put into a talk outline and/or someone in the Writing Department to have it put into a magazine article. Otherwise they rubberstamp the orders from the corporate-types above or the suggestions from the Department heads below.
Now the Department Heads (Committee Elders I think they are called) may have some authority because they have actual people working for them who they get to boss around. But they can't really change doctrine, not without permission. They can only create clever new ways to explain and enforce the doctrines on the rank and file JWs.
Your Branch, District, and Circuit Overseers are next, in that order. They all do what they're told or they're replaced. But they can bully elders both locally and at the assembly/conventions, so that gives them a bit of an ego boost.
The local elders hold your life in their hands. If you don't realize you have to kiss their ass you are in danger of being a free thinker and probably won't live out your whole life as a JW. You're already on your way out. If you want to stay IN, you will obey the local elders WITHOUT QUESTION. (I questioned, got counseled, it pissed me off enough to do research, and I left - there's just one anecdotal piece of evidence for you)
Beneath the local elders are anointed brothers. They have no authority at all because like their heavenly counterparts, they are not allowed to DO ANYthing. They do get to drink a sip of wine and eat a cracker once a year though, so they've got that going for them.
Beneath the anointed brothers comes Ministerial Servants. These are volunteer slaves. They do what they're told by the elders or they're replaced.
Beneath Ministerial Servants are baptized brothers. These can be any age (usually between 8 and 100), as long as they have been baptized. They have no real authority unless there are females around.
Beneath baptized brothers are anointed sisters. These are just like anointed brothers but they're women. They will never be more than they are.
Beneath anointed sisters are regular baptized sisters. These are the lowest rank on the JW ladder. The only "priviledge" they qualify for is pioneering and cleaning.
Which brings up pioneering. This isn't a separate rank because people from all ranks can be pioneers. But if you ARE a pioneer, you get a little bump in prestige, though no real extra juice.
So that summarizes the JW "Class" system as it currently stands. The anointed could be divided into pre-1935 and post-1935 but really there aren't enough pre-1935 anointed still alive to be concerned with.