The short answer is New Balance, more precisely, the 990 range (He wore the 992 most of the time). The long answer is a little more interesting however. Why did he pick this particular model? Why did he always wear the same outfit and why did he prepare to walk barefoot?

Why the NB 992s?
New Balance had been around for quite a few decades before Apple was founded and they did not become mainstream until the 80s, so why did he pick this footwear specifically? It turns out Jobs himself actually played a role in the creation of the NB 992. New Balance chairman at the time, Jim Davis, explained that Jobs wrote him a letter explaining what he wanted in a shoe, going as far as including a drawing in the letter. Those ideas and drawings were actually one of the sources for the NB 990 line and the rest is history.
New Balance shoes are still very popular today because they are simply comfortable, reliable and durable shoes, you know that they can take a beating without skipping a beat.
Why did he wear the same outfit all the time?
The idea to wear an “uniform” on a daily basis came to Jobs in the early 80’s when he visited Japan. He first tried to introduced the idea of wearing an uniform at a wider scale at Apple, however, that idea was not well received at all, in the end, he decided to adopt one for himself and asked the Japanese designer Issey Miyake to create one for him, and thus the famous black turtleneck T-shirt was born. Jobs complemented it with Levi’s 501 jeans and a pair of New Balance 992s and the rest is history, he wore that same style of outfit for many years to come.
Why did he like to be barefoot whenever possible?
New Balance shoes are nice, but what he liked the most was actually walking barefoot, and it all originated from his Buddhism influences. Zen practices were very important for him, things like eating raw vegetables, fasting and veganism. Walking barefoot was an integral part of his beliefs.
Are they still available today?
New Balance 992s are still available today at most retailers for around $135 a pair.