On EU-level it depends on whether your slogan is merely
perceived as a promotional formula or if it is also
considered an indication of commercial origin - if the
latter is the case, then the answer is yes, your slogan can be
registered as a trademark.
A trademark's purpose is to indicate the origin of specific
goods and services and thereby allow the consumers to distinguish
between different undertakings. In order to fulfill this purpose, a
trademark must have distinctive character.
This is where it gets a bit tricky for slogans (compared to
i.e., logos) since slogans, rather than being perceived as
indicators of origin, are generally perceived by consumers as
nothing more than commercial instruments in the marketing of goods
and service. For this reason, slogans are struggling to meet the
legal requirement of distinctive character.
