I'm particularly interested in famous individuals who have an identical twin who isn't famous. For example, movie star Jon Heder has an identical twin, Dan Heder, who isn't as famous, but I'm not exactly sure why Jon Heder is famous in the first place. (And I'm not sure he is either.) But that situation is relatively uncommon. Either both identical twins are famous or neither one is. And the percentage of famous people who are identical twins appears to be lower than the percentage of identical twins in the population.
Wikipedia offers a list of "Famous people with a twin," but most of the twins appear to be either fraternal and/or died young. For example, Elvis Presley had a twin brother, but he died at birth. (That's not uncommon on this list — carrying and delivering twins is tough.)
I suspect that to get famous in a lot of fields, such as acting (here's Wikipedia's list of twin actors — most of the names either aren't too famous or are fraternal twins) you have to elbow your way past a lot of people to grab the spotlight as you are growing up.
For example, a lot of well-known actresses were the stars of their high school musicals. That's a common rite of passage if you want to be a movie star someday. Say you and your identical twin sister want the role of Maria in your high school production of "Sound of Music." One of you would get Maria and the other would get stuck being the Head Nun. So, maybe you talk it over with your twin and decide neither will try out for it because it would be too painful for the loser. Or maybe the director feels uncomfortable choosing between you, so he gives the role to somebody else who isn't a twin.
I suspect that considerations such as this tend to discourage identical twins from pursuing a lot of careers with steep pyramids of fame.