Post Made Community Wiki by S. Carnahan
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As Craig Westerland points out, the space $V_n$ of full-rank $\infty\times n$ complex matrices (aka the infinite Stiefel manifold) works for any subgroup of $GL_n({\Bbb C})$. That applies to all the examples listed in the question, except the free group -- but of course, it's nice to have alternative descriptions, such as the ones given above, where it's easier to get a handle on $BG$. (A compendium of these things would be nice to have.) Here are a few more:

(1) For $G$ upper triangular matrices in $GL_n({\Bbb C})$, $EG=V_n$ gives $BG=Fl(1,\ldots,n;{\Bbb C}^\infty)$.

(2) For $G=({\Bbb C}^\ast)^n$, you can take $EG=(V_1)^n$ and get $BG=({\Bbb CP}^\infty)^n$. Or you could take $EG=V_n$ and get $BG$ as the space of $n$-dimensional subspaces of ${\Bbb C}^\infty$, together with a splitting into lines. The latter has the advantage of coming with an obvious map to the space from (1), realizing the homotopy equivalence explicitly. (I mention this to point out that it can be useful to have different choices available, even for "decomposable" groups.)

(3) For $G=Sp(2n)$ (the compact symplectic group), take $EG$ to be "full-rank" $\infty\times n$ quaternionic matrices, and get $BG = Gr({\Bbb H^n},{\Bbb H}^\infty)$. (It has the same cell structure as the complex Grassmannian, but with cells in dimensions $4k$ instead of $2k$.)

(4) For $G=Sp_{2n}({\Bbb C})$, you can take $BG=Sp_{\infty}/(Sp_{2n}\times Sp_{\infty})$ (interpreted as a suitable limit).