Do electron donating groups make a molecule nucleophilic?
Do electron donating groups make a molecule nucleophilic?


Sometimes. 

Sure, electron donating groups can make a molecule more nucleophilic by virtue of increasing the negative charge density on the nucleophilic atom.

However, nucleophilicity is a kinetic property, and having a lot of electron donating groups attached can significantly affect the ability of the nucleophile to approach the electrophile. This reduces nucleophilicity. An example would be tert-butoxide. Yes, oxygen with a negative charge is generally nucleophilic, and yes, the tert-butyl group is an inductive donor, but tert-butoxide is not very nucleophilic because of steric hinderance. 


  One group, the alkyl group in this example, is electron donating in $\ce{CH3CH2O-}$. Will the molecule be nucleophlic? 


Maybe. Nucleophilicity also depends on the solvent. A charged ion such as ethoxide ion would be well-solvated in a polar solvent, such as water, and less well-solvated in a non-polar solvent, such as hexane. 

Solvation impacts reaction kinetics, and in turn, impacts nucleophilicity. Consider the halides for example. In polar protic solvents, iodide ion is the strongest nucleophile. Protic solvents are not able to solvate iodide ion as well as they can solvate the fluoride ion, which has a much higher negative charge density. In polar aprotic solvents, however, fluoride ion is generally a stronger nucleophile than iodide ion because fluoride ion is not as strongly solvated and it also has a great negative charge density. 

In sum, nucleophilicity is not an inherent property. It depends on a variety of factors - both external and internal to whatever molecule or ion that you are considering.