Never leave home without it.
And as other people have mentioned for the absolute basics you will need a good set of metric allen wrenches, chain tool, tire levers, and pump. Additionally, it's good to have a
chainring nut wrench. Oh, and a tub of grease.
Beyond the basics, if you start doing more of your own work, you will need a lock ring wrench, chain whip, crank puller, bottom bracket tool, headset wrench, and spoke wrench.