1.A big sharp axe!! !! for killing zombies, and smashing in doors etc...
2.A big rucksack. For carrying miscelanous items in....
3. A set of lock picks. So I can steel a car, or break in to a building and hole up.
In the event of a zombie apocalypse, I would heavily fortify my house, sandbagging and barricading all doors, windows and weaker walls. before doing so I would stock up on loads of food, get a gun, ammunition and many other items for defence. Finally, I would get a generator and hook it up to my houses main power.
Then, I would wait it out! and since windows would be barricaded, the zombies wouldn't know I was there, and eat my neighbours, not me, and I would spend a long time on the computer or something! When I needed more food, I would steal form the shop down the street, or maybe use our car to get to ASDA, armed with a gun, ammo, an axe, and a big bag for food! While gone from my house I would have a ladder in the hedge outside my house, and a upstairs window open a fraction. So I would return, and get inside and not exit for another couple of months...