“Let’s give each European residing in another European country the right to vote; not only in municipal and European elections but also in regional and national elections of his country of residence”, claims the initiative on www.letmevote.eu. The goal of the initiative is to develop the political dimension of the European project by reinforcing citizens’ awareness that they share a common destiny.
According to the initiators this would have the following effects: – To enhance the concept of European Citizenship; – To facilitate freedom of movement within the EU; In addition, it could contribute to remedying the loss of voting rights presently experienced by a significant number of EU citizens who are long-term residents of other Member States

“Let me vote” has committees in seven member states of the European Union – Belgium, France, Germany, Italy, Luxembourg, Netherland, Spain - and is now on the list of open initiatives. Deadline for the collection is 28th January 2014

Article 20 TFEU
1. Citizenship of the Union is hereby established. Every person holding the nationality of a Member State shall be a citizen of the Union. Citizenship of the Union shall be additional to and not replace national citizenship.

2. Citizens of the Union shall enjoy the rights and be subject to the duties provided for in the Treaties. They shall have, inter alia:
(a) the right to move and reside freely within the territory of the Member States;
(b) the right to vote and to stand as candidates in elections to the European Parliament and in municipal elections in their Member State of residence, under the same conditions as nationals of that State; C 115/56 EN Official Journal of the European Union 9.5.2008
(c) the right to enjoy, in the territory of a third country in which the Member State of which they are nationals is not represented, the protection of the diplomatic and consular authorities of any Member State on the same conditions as the nationals of that State;
(d) the right to petition the European Parliament, to apply to the European Ombudsman, and to address the institutions and advisory bodies of the Union in any of the Treaty languages and to obtain a reply in the same language.
These rights shall be exercised in accordance with the conditions and limits defined by the Treaties and by the measures adopted there under.

More open initiatives are registered here 
Guide to the European Citizens’ Initiative.

Image: © European Union 2012 - European Parliament