#1. Running Shoes - ie. A good pair of Nike running shoes. Just do it.
#2. Comfortable Pants or Shorts - If its winter you will want something you can run in easily and has some kind of deep pocket to keep your house/apartments keys in so you don't get locked outside. (Speaking for myself, I wear camouflage army pants with big pockets.)
#3. A Hoodie - Because nothing says jogging like running around like Rocky Balboa in matching grey pants and hoodie.
#4. Gloves - If you're jogging in the winter comfortable warm gloves is a must.
#5. Scheduler - It doesn't matter whether you use a calendar, your alarm clock on your cellphone or a fancy dancy device specifically for joggers. Anyone who tracks their jogging is more likely to turn it into a routine and become successful in their goal of losing weight, running marathons, etc.
#6. Music - This is really optional, but a mp3 player or old fashioned walkman works just as well if you need extra motivation. I recommend including several songs from the Rocky soundtrack just for fun.