So I played around. Yeah it seems DSolve recognized something with the ICs that it liked. So that isn't helping you much. However, this might help you with some tricks related to the infinite series. Also notice I used DSolveValue to avoid getting back a rule.

weqn = D[u[x, y, t], {t, 2}] == Laplacian[u[x, y, t], {x, y}];
ic = {u[x, y, 0] == (1/10) (x - x^2) (2 y - y^2), 
   Derivative[0, 0, 1][u][x, y, 0] == 0};
bc = {u[x, 0, t] == 0, u[0, y, t] == 0, u[1, y, t] == 0, 
   u[x, 2, t] == 0};
dsol = DSolveValue[{weqn, ic, bc}, u, {x, y, t}];
ListAnimate[
 Table[Plot3D[
   Activate[dsol[x, y, t] /. Infinity -> 5], {x, 0, 1}, {y, 0, 2}, 
   PlotRange -> {{0, 1}, {0, 2}, {-0.05, 0.05}}], {t, 0, 10, 0.25}]]

Note the Activate function and the replacement of infinity.

I realize you want a nice compact equation, but you might not get it.

Sounds like progress. I'll play around a bit more when I get home from work.

Thanks for the replys! NDSolve is really interesting and the animations are great, but i would also really like to take a look at the analytical solutions for these equations. I tried some ic's (plane waves,gaussians,..) in 2D, now with the 4 bc's, but everytime i just got my input as output, without an error message (as with your codes).I've found something in the DSolve documentation though, under Scope->Hyperbolic PDEs, quote:

Dirichlet problem for the wave equation in a rectangle:

weqn = D[u[x, y, t], {t, 2}] == Laplacian[u[x, y, t], {x, y}];
ic = {u[x, y, 0] == (1/10) (x - x^2) (2 y - y^2), 
   Derivative[0, 0, 1][u][x, y, 0] == 0};
bc = {u[x, 0, t] == 0,
    u[0, y, t] == 0, u[1, y, t] == 0, u[x, 2, t] == 0};

The solution is a doubly infinite trigonometric series:

(sol = FullSimplify[
    u[x, y, t] /. DSolve[{weqn, ic, bc}, u, {x, y, t}][[1]], 
    K[1] \[Element] Integers && 
     K[2] \[Element] Integers]) // TraditionalForm
\!\(\*
UnderoverscriptBox[
StyleBox["\[Sum]", "InactiveTraditional"], 
RowBox[{
TemplateArgBox[
RowBox[{"K", "[", "1", "]"}]], "=", 
TemplateArgBox["1"]}], 
TemplateArgBox["\[Infinity]"]]\(\*
UnderoverscriptBox[
StyleBox["\[Sum]", "InactiveTraditional"], 
RowBox[{
TemplateArgBox[
RowBox[{"K", "[", "2", "]"}]], "=", 
TemplateArgBox["1"]}], 
TemplateArgBox["\[Infinity]"]]\*
TemplateArgBox[
FractionBox[
RowBox[{"32", " ", 
RowBox[{"(", 
RowBox[{
SuperscriptBox[
RowBox[{"(", 
RowBox[{"-", "1"}], ")"}], 
RowBox[{"K", "[", "1", "]"}]], "-", "1"}], ")"}], " ", 
RowBox[{"(", 
RowBox[{
SuperscriptBox[
RowBox[{"(", 
RowBox[{"-", "1"}], ")"}], 
RowBox[{"K", "[", "2", "]"}]], "-", "1"}], ")"}], " ", 
RowBox[{"cos", "(", 
RowBox[{"\[Pi]", " ", "t", " ", 
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"K", "[", "1", "]"}], "2"], "+", 
FractionBox[
SuperscriptBox[
RowBox[{"K", "[", "2", "]"}], "2"], "4"]}]]}], ")"}], " ", 
RowBox[{"sin", "(", 
RowBox[{"\[Pi]", " ", "x", " ", 
RowBox[{"K", "[", "1", "]"}]}], ")"}], " ", 
RowBox[{"sin", "(", 
RowBox[{
FractionBox["1", "2"], " ", "\[Pi]", " ", "y", " ", 
RowBox[{"K", "[", "2", "]"}]}], ")"}]}], 
RowBox[{"5", " ", 
SuperscriptBox["\[Pi]", "6"], " ", 
SuperscriptBox[
RowBox[{"K", "[", "1", "]"}], "3"], " ", 
SuperscriptBox[
RowBox[{"K", "[", "2", "]"}], "3"]}]]]\)\)

End of quote. Why does this work and the others don't? The only difference i can see are the initial conditions?

Interesting.

I don't get an error message, but neither a solution.....

DSolve[{-
\!\(\*SuperscriptBox["u", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "0", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, y, t] + 
\!\(\*SuperscriptBox["u", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, y, t] + 
\!\(\*SuperscriptBox["u", 
TagBox[
RowBox[{"(", 
RowBox[{"2", ",", "0", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, y, t] == 0, 
  u[x, y, 0] == E^(-x^2 - y^2), 
\!\(\*SuperscriptBox["u", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, y, 0] == 0, u[x, 0, 0] == 0, 
  u[0, y, 0] == 0}, u, {x, y, t}]