My vote would be for Die Hard. DH1-3 are great films with 4 being ok.
Indiana Jone 1 and 3 are great films, 2 is good but not great and 4 has Shia Le-mahogany, monkeys, gophers, nuclear explosions, bloody aliens, a nonsensical plot, Russians (just not as good as Nazis) and did I mention bloody aliens? Harrison Ford made it seem like it hadn't been 20 years but was let down by a crappy script.
Terminator 1 and 2 are both great films but 3 and 4 are bad films.
The Mummy? I agree it shouldn't even be mentioned in the same company as the other series. The first film was good but the second had a terrible plot and worse special effects and the third one was just meh.
Best film though is and always will be Raiders Of The Lost Ark.