As for every embroidery you'll need a needle. It can be any that will suit the thread, however if you have a few pennies/ cents to be spent you can buy the needles with a blunt point. They're called tapestry needles. I use the ones with the no. 22 and 24 to match the 5 i 8 pearl cotton threads. So far I only tried the Clover brand so cannot compare to other ones, but I'm pleased with them.
Second thing is the scissors - as the bulk of the work with hardanger is cutting the threads from the fabric. I used the typical scissors for hand embroidery with slim blades. The second cutting tool that I bought and highly recommend is the thread clipper. Not only it's much faster to cut the thread from the ball or skein but it's also very convenient for the drawn-thread embroidery techniques. I bought the Clover one (again) and it was....well, it wasn't cheap. Recently I saw similar one in a shop which costed a couple of PLN (about 1,5$). The difference in price shocked me a bit, but I want to believe that Clover one was worth its price and will serve me for years :). Anyway, regardless of the brand I think the thread clipper is a very useful tool for variety of embroidery techniques.