A door will solve it

How about some nice print curtains? Not too heavy so they can slide to the side when your doing laundry. It might help with noise too.

My laundry room looks similar. How about 2 white folding doors. The closet doors with the slots is what we have.

I was thinking of the barn doors too. They won't take up as much space when open as a conventional door and they hide your laundry area nicely when not in use. And I am suggesting this even though I think barn doors have been used by everyone waaaay too much but in this space I think it would be a perfect tidy solution.

and for a more economical solution you could also use those curtain panels that Ikea has. You know the straight, flat ones. http://www.ikea.com/ca/en/catalog/categories/departments/Textiles/10702/

I agree with curtains! Perhaps something colorful and fun!

I think curtains hung where doors need to be is just tacky so my vote would be barn doors if you have the space.

What did the "horribly ugly" doors look like? Could they be refinished/repainted to improve the appearance? Probably your most economical fix and certainly better than no door at all. And no doubt a whole lot better than a curtain.