Donaldson-Thomas invariants have recently attracted the attention of mathematicians interested in GromovWitten theory, because of a new conjecture (the MNOP-conjecture) relating the two theories. Donaldson-Thomas invariants are special, because the corresponding moduli spaces are sets of critical points of certain Chern-Simons type functionals. Because of this, they should be related to Euler characteristics of the corresponding moduli spaces. We explain a conjectural approach to define within algebraic geometry certain Euler characteristics, which are equal to Donaldson-Thomas invariants. As an application, we obtain (conjecturally) Donaldson-Thomas type invariants for non-compact moduli spaces.