You can search Chamber of Commerce and Industry in your country---may be they have such sources,

Can you be specific in your question? database is a broad word and SMEs exist everywhere but you need to be precise in your questions so others can help you in a better way

With database I mean a list of SMEs respecting European criteria to be called so with the most amount of information about the company (name, adress, industry, year of founding, # of employees, founders, administrators,...)

Thanks for your answers

I think the needed data may easily be arranged from the regulating body of these SMEs in your country.However,keeping in mind the capital requirements and other limits,there may arise a difficulty in getting the whole of the data.However, the reliable and accurate data may be there with the regulating agencies,and or trade associations.

Interersting field of study.

Sanjeev's reply is useful.

In India it is difficult to get SME data as you require. Ministry of MSME and a few industry associations publish data, though generic. Registrar of Companies provide paid info about financials of pvt. ltd. Companies.

Before you going to collect data of SME, make sure what definition of SME you want to use. There is no international consistent definition. For example in Germany there are at least three common definitions: EU Commission, national law (HGB) and IfM Bonn (SME and Family business research institution).

GEM

http://www.gemconsortium.org/

Generally such databases are unlikely to find even though, I think, all of SEM researchers would welcome them :-)

Situation may vary from country to country so you need to specify which country you are targeting and perhaps then you will obtain more specific answers.

In Poland some of the data, but certainly not all, can be purchased from main statistical office. These will be anonimized so they make little sense if you want to acquire additional data related to the same companies (like performance).

You can try to use commercial databases Kompass, Dun&Bradstreet and similar too but of course these will not be exhaustive, particularly for SMEs and will cost money.

I agree with Anwar Shah that Chambers of Commerce and business associations might be a useful source.

There are a number of datsets available look at OECD, Unesco, Federation of Small Business. Gem as identified above.