One of my favorite songs has only one rhyme (barely), but i think it is one of the best written songs I have ever heard (ok, maybe just one of the funniest!).
It's "Frank Mills" from the musical "Hair" That song works very well. I think (at least in western music) that, while rhyming is important, meter is much more important, and a well structured song can get by with a minimum of rhyming.
However (here it comes), it seems that more and more, people are unwilling to "work" to understand songs. The song has to almost 'pre digested", as it were, before any one will even seriously pay attention to it. If you doubt this, just play Robert Johnsons "Love in vain" for the average music consumer today and watch their reaction.
They won't get it. They'll wonder why on earth you are wasting their time with that stuff.
So, it seems you also have to consider the sophistication of your audience as well.