I am looking for a list of classifying spaces $BG$ of groups $G$ (discrete and/or topological) along with associated covers $EG$; there does not seem to be such cataloging on the web. Or if not a list, just some further fundamental examples. For instance, here are the ones I have off the top of my head:
$B\mathbb{Z}_n=L_n^\infty$ with cover $S^\infty$ ($B\mathbb{Z}_2=\mathbb{R}P^\infty$)
$B\mathbb{Z}=S^1$ with cover $\mathbb{R}$
$BS^1=\mathbb{C}P^\infty$ with cover $S^\infty$
$B(F_2)=S^1\vee S^1$ with cover $\mathcal{T}$ (infinite fractal tree)
$BO(n)=BGL_n(\mathbb{R})=G_n(\mathbb{R}^\infty)$ with cover $V_n(\mathbb{R}^\infty)$
$B\mathbb{R}=\lbrace pt.\rbrace$ with cover $\mathbb{R}$
$B\langle a_1,b_1,\ldots,a_g,b_g\;|\;\prod_{i=1}^g[a_i,b_i]\rangle=M_g$ with cover $\mathcal{H}$ (hyperbolic plane tiled by $4g$-sided polygon)
And of course, $B(G_1\times G_2)=BG_1\times BG_2$, so I do not care that much about ''decomposable'' groups.
**The "associated cover" is the [weakly] contractible total space.
[Edit] I should make the comment that $BG$ will be different from $BG_\delta$, where $G_\delta$ denotes the topological group with discrete topology. For instance, the homology of $B\mathbb{R}_\delta$ has uncountable rank in all degrees (learned from a comment of Thurston).
