How strong an influence has Led Zeppelin had on heavy metal bands?

I'm not sure if I would classify them as heavy metal but I do feel that they heavily influenced heavy metal groups. Perhaps you could say that they were the grandfathers of heavy metal. I don't think heavy metal would have happened if they hadn't developed such a heavy sound.

It seems like I have heard that also they are a great band.

I think that their influence is more an indirect influence then direct. I wouldn't say Zeppelin was the first metal band.. I'd give that to Sabbath. If they influenced indirectly it may be an influence that they had on a band like Black Sabbath who then influenced other metal bands directly.

First of all, it is fairly irrelevant as to what they say. ACDC has always called their music "rock'n'roll" even though usually that term is either attributed to rock in general or 50's rock'n'roll. I also seem to recall that at least some members in the band rejected the term heavy metal, so it seems rather contradictory of Robert Plant to make that statement. Now, as for my opinion, I don't think Led Zeppelin was heavy metal. They definitely influenced metal bands, but they were still either hard rock at the fiercest or something softer. The first heavy metal band in my opinion is probably Black Sabbath, though Judas Priest spawned a faster version compared to Sabbath's doomy atmospheres.