Grammatical vs. natural gender

When my (American) wife learned German, I understood for the first time the difficulties posed for English speakers by the gender of German nouns, which, with very few exceptions, has nothing to do with "natural" gender. For example, a sausage (Wurst) is feminine, but an umbrella (Schirm) is masculine--how can this possibly make sense to someone for whom both are neuter? After all, there is nothing inherently "masculine" or "feminine" about either. This thread intends to explore this issue further.