I know these people:

1)Panait Istrati (an excellent author)

2)Emil Cioran (an excellent philosopher)

3)Nicolae Iorga (an excellent historian)

4)Gheorghe Hagi (an excellent football player)

5)Gheorghe Popescu (an excellent football player)

6)Vlad Tepes (Dracula) 

Laurentiu Panaitopol, who was one of the greatest Romanian Math teachers.

Nadia Comăneci,

a Romanian gymnast, winner of three Olympic gold medals at the 1976 Summer Olympics, and the first gymnast ever to be awarded a perfect score of 10 in an Olympic gymnastic event. She is also the winner of two gold medals at the 1980 Summer Olympics. She is one of the best-known gymnasts in the world and, along with Olga Korbut, is credited with popularizing the sport around the world.[1][2][3] In 2000 Comăneci was named as one of the athletes of the century by the Laureus World Sports Academy.

Well, of course:

Adrian Mutu

Adrian Ilie

Lucescu

Lacatus

Rotariu

In addition to aforementioned. Among politicians, I still remember Ceausescu (though I am still not sure about the spelling.) The most renowned Romanian must be Dracula by the way.

I can think of two names only:

Vlad the Impaler - the funny thing is, a group of friends and I were going through Romania and since we were on the Transylvanian Route, we wanted to see Dracula´s castle. Unfortunately it was way before mobile internet so we had to ask locals. None of them knew who we were talking about. They said there were many Vlads and they didn´t know which one we meant. Dracula didn´t tell them anything and neither did my impersonation of a vampire. It was hard to believe they wouldn´t know him, unless they were just taking the mickey...

and

Nicolae Ceausescu - that´s because we´re from the same communist block of countries

Wikipedia already has it:

Famous Romanians

Edit:

Hmm, going through the list, it appears that I forgot to mention famous tennis player Nastase and chess player Nisipeanu. And of courese Gabriela Szabo from atletics section.

Also I see two people with their names ending -oglu (a Turkish suffix) in Math people.

I don´t personally know any famous Romanians - however other famous Romanians I have heard of:

Ilie Nastase (excellent former World No. 1 tennis player in 1970s)

Eugene Ionescu (playwrite Theatre of the Absurd)

Edward G Robinson (actor/filmstar) (wow! i learnt something today!!)

zeytinne, elenagabriela, her daughter, late Ceausescu and his wife..

What is next?  Famous people of Papua New Guinea? exotic  animals of Guinea Bissau?

Dimitrie Cantemir ...this for turks

It is better knowing new people than always discussing about Kurdish and Armenian issues over and over again.

I always wanted to read Mircea Eliade´s books about religions and mythology but always other books  intervened.