From the articles linked in the comments:
Parameter Bound Effects Experiment
--------- ----- ------- ----------
γ − 1 2.3 x 10^-5 Time delay, Light deflection Cassini tracking
β − 1 2.3 x 10^-4 Nordtvedt effect, Perihelion shift Nordtvedt effect
ξ 0.001 Earth tides Gravimeter data
α1 10^-4 Orbit polarization Lunar laser ranging
α2 4 x 10^-7 Spin precession Sun axis' alignment
with ecliptic
α3 4 x 10^-20 Self-acceleration Pulsar spin-down
statistics
ζ1 0.02 - Combined PPN bounds
ζ2 4 x 10^-5 Binary pulsar acceleration PSR 1913+16
ζ3 10^-8 Newton's 3rd law Lunar acceleration
ζ4 0.006 - Kreuzer experiment
Where the parameters are so defined:
The parameters $\gamma$ and $\beta$ are the usual Eddington–Robertson–Schiff parameters used to describe the “classical” tests of GR, and are in some sense the most important; they are the only non-zero parameters in GR and scalar-tensor gravity. The parameter $\xi$ is non-zero in any theory of gravity that predicts preferred-location effects such as a galaxy-induced anisotropy in the local gravitational constant GL (also called “Whitehead” effects); $\alpha_1$, $\alpha_2$, $\alpha_3$ measure whether or not the theory predicts post-Newtonian preferred-frame effects; $\zeta_1$, $\zeta_2$, $\zeta_3$, $\zeta_4$, measure whether or not the theory predicts violations of global conservation laws for total momentum.
And these are the GR-predicted values:
γ = β = 1 and α1 = α2 = α3 = ζ1 = ζ2 = ζ3 = ζ4 = ξ = 0
