The last time Dog was at the house I tried Vegemite. I had it on a piece of toast with real butter and just a thin spread of Vegemite on top.
It is a bit salty, with a touch of yeasty flavor that is almost beef like. It helps to think of it as a condiment that enhances the flavor of other stuff kind of like we use hot sauce down here in the South.
I could see where it would be good in soups, stews, chili, sandwiches, etc... as a flavor enhancer. Personally, I liked it on toast with butter. I think it would be great on a BLT sandwich too.
I think where most Americans get off on the wrong foot with Vegemite or Marmite is that they think of it more like a savory jam or jelly, and that's just not the way to approach your first tasting. It's better to think of it more like vegetarian potted meat.