Most definitely without a doubt, unequivocally YYYYEEEESSSS!
You can get away with it for a two tier cake, specially if the top one is only six inches or so, but it can effect the look and also makes cutting a pain. Anything over two tiers - I wouldn't even try it.
For my 3 - 5 tier wedding cakes I use cake board (cardboard or plastic, depending on the design). I use dowels with cardboard in the lower tiers (if I want to raise or slightly tilt the next tier I use plastic plates and tubes). For something like a topsy turvy that is three or more layers I stick another dowel straight down the centre.
Now, this is me. But I think you will find other cake designers/artists do much the same thing. For every video or instruction site that says not to, you will find one or two that say it is definitely necessary.
Hope that helps!