I can't think of any bands that "grew on me", really, but there are a few albums:
The Velvet Underground's self titled. After having furiously rocked out (or whatever verb is appropriate to the Velvets; shot up skag, perhaps?) to The Velvet Underground & Nico and White Light/White Heat, I was initially angered and confused by the 1968 self titled. What is this soft, pansy music? At first I could only tolerate "The Murder Mystery", because it reminded me of "The Gift". It spent a long time collecting dust in the CD holder.
But then one day, about a month ago, bored and lacking in inspiration, I dug it out and threw it into the computer. Sure, it bore little resemblance the previous two albums, but it was amazing in its own way. "What Goes On", "Pale Blue Eyes", and, yes, even "After Hours". Maureen Tucker's girlish vocals give it an innocence rare in the VU's catalogue.
And just a few weeks ago I bought Loaded, which is in a similar vein (tee hee).