They did. Ever hear of the Zeppelin? They took off all the time in their hey-day. It's a myth that they were filled with hydrogen; the Hindenburg was only had hydrogen in it because at the time helium was not available in Germany at the time because it was only produced in the United States and the US was refusing to export it.

Anyway, the reason we don't see airships much anymore is because for most things heavier than air craft are more economical. A Boeing 747 is a third the size of a Zeppelin but much faster, more reliable, and with much more usable space and lifting capacity. There's really no economic reason that an Airship should be preferred.