Bad Company is one of the 3 most famous signees to Led Zeppelin's well renown "Swan Song" record label--The aforementioned Zeppelin(plus early 80's solo releases from Page & Plant) and BadCo, plus blues-based guitarist Dave Edmunds. Of the two bands(I do not know enough about Edmunds to judge), I definitely prefer BadCo to Zeppelin.
Good as their hits are, some of their less-than-renown material is quite meaningful. Quite a few of those songs were featured on their latest live album, probably more because of the then-recent(at the time of the concert performances) issuance of the "Burnin' Sky" and "Desolation Angels" albums than anything else.
Some of my favourites: https://www.youtube.com/watch?v=ixwgJFB6Pks
https://www.youtube.com/watch?v=r5p1ueLiIlo
https://www.youtube.com/watch?v=b3k7mfRexxo
Aside from their most obvious song, I don't know a whole lot about the band Free.