Thompson's group F (http://en.wikipedia.org/wiki/Thompson_groups) is also an example: it isn't virtually solvable (actually, its commutator subgroup is simple) and does not contain a free subgroup, according to a theorem of Brin and Squier ("Groups of piecewise linear homeomorphisms of the real line.", Invent. Math. 79 (1985))).
Maxime Bourrigan
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