I haven't used it myself, but I've been told there is paint that you can use to paint over porcelain/ceramic tiles. Then you can go with any color you want! Good luck - and be sure to post "after" pictures!

Try this: http://www.rustoleum.com/product-catalog/consumer-brands/transformations/tile-transformations/

Years ago I had a company come and paint some tile and counters for me I would not recommend it for counters but the walls are fine. They used an epoxy paint and I would recommend having a professional come in and do it rather than trying it yourself that epoxy paint is hard to work with and they have the sprayers to make it look like a professional job. It was a long time ago I had this done but I believe they didn't charge me more than a couple hundred dollars per bathroom.

I know you said the blue tile has to stay - but can you cover the it with wainscoting?

A slate gray might help. Mirrors and art on the wall might help draw attention away from the tile as well.

I like the slate gray idea. If you paint the cabinet white(use the rustoleum as mentioned), you can get a new vanity top with sink at any big box store. I have not used these tile "tattoos" , but they look intriguing.

You can have mirror cut to size and stuck over the tiles. It adds light, humour a but of fear and a definite design!

Embrace the blue. I like the bold colors silk posted. No one will be looking at the tiles, they will be enjoying the paint color!

I had a bathroom in a prior home years ago when faux finish was the rage the bathroom had sort if a orange tile. I worked that color into the faux finish and my guests always loved it. You would be surprised with what you can do buy just updating the wall color to draw attention away from the tile.

I like both the suggestions of D.S. Brennan Photography and silk789, painting the upper wall a bold deep blue or gray and a nice big mirror would draw the attention upwards and away from the tile.

Painting the tile looks good for a while, but any scratches will show if it is a completely different color from the tile and it will get bigger with time and paint will start to peel off from them (a touch up every now and then on those should do the work for a while). Be sure there isn't any humidity since it peels off more easily that way, though it is a powder room so I don't think it will happen.

Anyway, painting is a good option if you want a quick and easy change and plan to remove it later. I would paint them maybe white or a light grey paired with the suggestions above.