In the days of film, it was a disaster to run out of film. In the digital age, it's a disaster to run out of batteries. It might be prudent to carry an extra memory card with you as well. They're inexpensive and take up no room at all. But if you don't have an extra memory card and run out of room, you can always delete photos that are obviously rejects or send some via wifi and keep shooting. If you run out of energy, however, you're in hot water, your goose is cooked, you're shot. As a general rule, you'll need an extra battery only when the conditions for shooting are ideal. If the conditions aren't that great, you'll take a few shots, maybe 50 or 100 and then pack it up and go home. Not much happening today. The next day opportunities are all around you and you come home with 400 or 500 shots, maybe more. If your battery is good for 250 shots or so, you better have an extra somewhere on your person or you'll be missing lots of shots.
If you're like me, there have been plenty of times when you've run out of energy and were frustrated you didn't have an extra battery. The worst was when I first started getting into photography while visiting Chicago in 2013. I had only one battery which would always conk out about 11 in the morning. That left a whole afternoon and evening without a camera. If you know anything about Chicago, you know it's a great place to take photos, especially in the summer when everyone is out on the streets and opportunities are all around you. I started carrying my charger with me and would slip into a coffee shop for two or three hours to charge up my battery. That would give me half a charge, maybe not even that much. As soon as I got back home to Hawaii, I ordered a second battery and have carried an extra ever since.
My experience has been that good photos come in clusters. The situation is interesting, the light is just right, you're seeing photos all around you. Those are the moments we have to be most opportunistic. I wish every day was as splendid as this, but they're not. Even in Hawaii there are plenty of days when it rains or when it's hazy, when the streets are pretty empty (except for Waikiki), and you're not feeling it. Take full advantage of those ideal days by making sure you have all the energy you need to power your digital camera.
For the last few years, I've been leaving the camera on the whole time I'm hunting for shots. Since most street photography isn't posed, you have to be ready in an instant to take a shot. If you wait even two seconds to turn on your camera, the moment's over. That's not always true, but it's true often enough for me to keep my camera on all of the time now. All I do is lift the camera up and start shooting. Now I just need a camera with faster auto focus!
Spare batteries can be expensive, but I've had good success buying them used from places like Amazon, Adorama or B&H. The cost is only a fraction of a new battery. I just bought a battery from Amazon, for instance, that was almost $40 new but was $12 used, including postage. Sure, you always have to be careful when buying used, but places like Adorama and B&H will rate the battery to give you a better idea what you're buying. I always buy batteries from the same company that made the original battery. Maybe generic brands are just as good, but I don't want to take a chance. And if you buy batteries used (or new with damaged packaging), the price can be the same or lower for original batteries. So keep at least one extra battery on you when you go out shooting. If you don't, you'll be sorry.