Wikipedia says:
In the Catholic Church, the Pope is regarded as the successor of Saint Peter, the Apostle.
cf. Pope | Wikipedia
As someone who isn't Catholic I don't want to argue how true this is or how significant this is.
What I'm interested to know is there an office/title/person in the Catholic church for any of the other 11 Apostles (12 if you include Paul), or is it just Saint Peter because he was the leader of the apostles?
The other apostles are associated with other Churches. St Mark, for example, was the founder of the Church of Alexandria; St Thomas is believed to have taken Christianity to India; and so on. Only St John the Evangelist did not die a martyr in a far-off place (at least, Patmos isn't as far as India).
Accordingly, most of the other apostles do not have such a place as Peter's within the Roman Church, but they do have a similar position as Patriarchs of the Churches they founded.
Apostolic succession applies to all successors of the original 12 apostles. Every modern day bishop and priest (including the Pope) has been ordained by Bishops, creating an unbroken lineage all the way back to the original 12.
This wikipedia section has it right, as far as I've read.
In Roman Catholic theology, the doctrine of apostolic succession states that Christ gave the full sacramental authority of the Church to the Twelve Apostles in the sacrament of Holy Orders, making them the first bishops. By conferring the fullness of the sacrament of Holy Orders on the apostles, they were given the authority to confer the sacrament of Holy Orders on others, thus consecrating more bishops in a direct lineage that can trace its origin back to the Twelve Apostles and Christ. This direct succession of bishops from the apostles to the present day bishops is referred to as apostolic succession.
-- http://en.wikipedia.org/wiki/Apostolic_succession#Catholic_Church
And as it states, Papal Primacy, which is what you're hinting at, is a different but related matter.
The primacy of the Bishop of Rome is an ecclesiastical doctrine concerning the respect and authority that is due to the Bishop of Rome from other bishops and their sees.
The questioner asked if there is an office or title of "apostle" in the Catholic Church, and seemed to want to know whether there are 12 of them, as in the primitive church. To my knowledge, neither the Catholic, Jewish, nor Protestant traditions recognize the calling/office of "apostle".
See also this related answer re hierarchy of order and hierarchy of jurisdiction in CC
What are the positions relative to each other in the Catholic church's clerical hierarchy?
I know of only one sect that does recognize the office or title of "apostle", and has 12 men currently holding that title. But it's not the Catholic Church.
