There are many datasets out there for phylogenetic trees, one can example can be found here.
However, I couldn't find something for phylogenetic networks. According to Wikipedia:
A phylogenetic network or reticulation is any graph used to visualize evolutionary relationships (either abstractly or explicitly)2 between nucleotide sequences, genes, chromosomes, genomes, or species.2 They are employed when reticulation events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved.
Of course a phylogenetic tree is a phylogenetic network, but phylogenetic networks can be thought of as rooted directed acyclic graphs, meaning that more complicated evolutionary structures can be captured.