I have looked at Test::Unit and Test:Class. Does anybody have any experience with these?

Yes (I wrote the latter :-)

What are other people using to create tests for complete software suites (as opposed to tests for just one module)?

Combinations of Module::Build, Test::Class, Test::Builder, Test::Harness::Straps and associated modules.

Are there any solutions for creating HTML reports (overview of failed tests, etc.)? Please share your experiences!

Take a look at Test::TAP::HTMLMatrix.