This is surprisingly tricky to express. The "titular de los datos" is the person whose data or details they are. It's referring to checking personal details of users, and the "titular" here is the user whose details are being checked. Very often "titular" can be translated as "owner" or "holder", but I don't think either will do here, because both have other meanings in the field of data protection:

"Data owner" means the "Person identified by law, contract, or policy with responsibility for granting access to and ensuring appropriate controls are in place to protect information assets."
"Data holder" is the person holding the data, but not necessarily or even usually the person to whom the data relate. It would normally be taken as a synonym of the technical term "data steward" or "data custodian", which means "An individual who is responsible for the maintenance and protection of the data".
http://www.calstate.edu/icsuam/glossary/def.shtml

The term we want is "data subject" or "subject of the data":

"Data subject
The data subject is the individual who the personal data is about, ie the subject of the data."
http://www.dft.gov.uk/vca/data-protection-act-guidance-on-co...

It's used equally in American English. It's used throughout the following document, for example, on the Minnesota Government Data Practices Act:

"Data Subjects’ Rights
Individuals about whom the government has data have the following rights:"
http://www.house.leg.state.mn.us/hrd/pubs/dataprac.pdf

"

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Note added at 16 hrs (2012-05-27 22:31:33 GMT)
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Could the "titular de los datos" refer here to the data owner, that is someone with responsibility for protecting and granting access to the data, rather than the data subject, the person to whom the data relate, the person whose data they are (the "person who the personal data is about")? I don't think so.

The context here is a draft legal provision referring to the granting of "títulos habilitantes" to gaming operators, the source of which I shall not reveal for reasons of confidentiality. Here it's talking about "datos obtenidos con anterioridad al otorgamiento del título habilitante", ie. personal data on users already held by operators. The preceding paragraph reads:

"La verificación de los datos de usuario de los que dispusieran los operadores de juego como consecuencia de una actividad desarrollada con anterioridad al otorgamiento del correspondiente título habilitante, no podrán ser verificados sin la previa obtención del consentimiento del titular de los datos.
Obtenido el consentimiento del titular de los datos, el operador procederá a la verificación de los mismos de conformidad con los procedimientos establecidos en esta Disposición [...]"

The data owner here is the "operador", who actually holds the personal data on "usuarios" and is thus required by law to protect it. The operator must obtain the consent of the "titular de los datos", so clearly the "titular" is the "usuario" whose personal data it is: the data subject.

This is how the expression "titular de los datos" is normally used:

"Titular Significa la persona física titular de los Datos Personales, o autorizada para entregar Datos Personales de un tercero conforme a las leyes aplicables, que entregue dichos Datos Personales al Responsable."
http://park-royalhotels.com/es/privacy
Here they are using the word "titular" to cover both the data subject and the data owner ("persona autorizada para entregar datos personales de un tercero"), but the expression "titular de los datos" is quite clearly the former, the person the data refer to.

"¿A que tiene derecho el titular de los Datos Personales?
A conocer, actualizar y complementar la información, que respecto a su persona esté contenida en bancos de datos, registros y archivos de la Universidad Veracruzana."
http://www.uv.mx/transparencia/preguntas/titular-datos-perso...

And so on.

Lay persons quite often refer to "the owner of the data" when they mean the data subject, possibly because they feel that morally each person "owns" his or her own personal data, or through ignorance of legal terminology. However, the UK's Data Protection Act refers consistently to the "data subject" when it means the person whose data they are. For example, section 7:

"7 Right of access to personal data.
(1)Subject to the following provisions of this section and to [F1sections 8, 9 and 9A], an individual is entitled—
(a) to be informed by any data controller whether personal data of which that individual is the data subject are being processed by or on behalf of that data controller."
http://www.legislation.gov.uk/ukpga/1998/29/section/7

And in many other places; similarly in US statutes. They only use the term "data owner" when they mean someone who legally holds personal data, and that's not what "el titular de los datos" means.

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Note added at 16 hrs (2012-05-27 22:59:57 GMT)
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It is also interesting to note that the expression "data owner" or "owner of the data" does not occur at all -- not once -- in the Data Protection Act 1998.
http://www.legislation.gov.uk/ukpga/1998/29

Moreover, although the Act does refer to "information", the term it uses consistently for what are called "datos personales" in Spanish is "data": after all, it is not called the Information Protection Act, and neither are comparable US statutes.

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Note added at 16 hrs (2012-05-27 23:11:16 GMT)
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"A "data subject" is any living individual who is the subject of personal data. [...]
A "data owner" is a person authorised to manage the processing of data on behalf of the University. Data Owners are named in a list maintained by the Data Protection Officer and published on the Computer Services website."
http://www.bathspa.ac.uk/regulations/data-protection/definit...