There is no such thing as an assault weapon. There are assault rifles, which are fully automatic, and there are rifles, which can be semi-automatic, lever action, bolt action, breach loading, etc. The term assault weapon was invented by the media to describe normal rifles that look like assault rifles. I digress....
To answer the question, yes. I'm going to assume by the phrasing and the picture that by assault weapon you mean AK-47's or AR-15's. They can be, but are not normally used for hunting, since most of the time, the law prohibits you from carrying a certain amount of ammunition in your rifle/magazine.
As for self defense? Absolutely, for many reasons. One reason would be that many of them (especially the AR-15) are lightweight, versatile and easy to use. It would be a lot easier for a woman to effectively use an AR-15 against one or many intruders than it would for say a 12 gauge pump shotgun or a bolt action rifle. Another reason would be if you had to defend yourself against a group of people or even the government. A good example of this is the Korean store owners during the LA riots in 1992. During the riots, business were being burned and looted, so a group of Korean store owners sat on the roofs of their business and defended their livelihoods against potential destruction. Since riots seem to be something that is gaining popularity as of recent events, it would do a lot of people some good to go out and purchase their own "assault weapon"
I assume you mean assault rifles (either semi or auto). While these are unneeded in hunting (at least in the US) and home defence (PDWs are far superior in home defence due to their shorter barrels). On the other hand, with the increase in pro life terrorism (arsons, threats, and murder of abortion doctors) some may need to arm themselves with something which packs a bigger punch. In recent years people who work at abortion clinics have become the victims of more and more terrorism and ultimatly they may need to defend themselves.
Where hundreds of criminals rampaged through the streets, looting and destroying businesses and even homes. If you lived there and a gang of 30+ thugs were trying to loot your store or destroy your house you would need a weapon like the ak47. You could not stop to reload every 10 shots, as the thugs would kill you.
In countries like Australia and America terrorism is a growing problem. In the last two months in my suburb in melbourne, australia, we've had an attempted beheading. Where the subject was shot dead, and two drive by shooting accidents. Maybe not assault rifles but appropriate weapons are 100% needed. And I personally don't think police are reliable to respond to your emergency quick enough.
The amount of time it takes for the police to arrive at the scene of a crime is slower than the average pizza delivery man. Now if you compare that to the time it takes to commit a serious felony like lets say murder and robbery there is a major gap between those two figures. Now throw an assault weapon into the mix and time falls into the home defenders court. Meaning that by the time the police show up you have apprehended the assailant yourself and have a nice hot pepperoni pizza ready for you and the officers to enjoy.
The term "assault weapon" is a very loaded term, and in my opinion doesn't have a definition. What makes an assault weapon? The fact that its semi-fire? Well, handguns are semi-fire too. Collapsible butt-stock? Most ak's don't have this feature. Standard 30 round capacity magazines? You can fit a 10 round magazine on any "assault weapon". To some people's standards you could put a pistol grip on a bat and they would consider it an "assault weapon". I digress.
I think when people use the term "assault weapon", they really mean "sporting rifle". A semi-automatic rifles; that either shoots .223, 5.56, or 7.62x39(rifle calibers) ect... I have used these calibers to hunt. You can, in my state, (oregon) use a sporting rifle to hunt. I use an ak that's chambered in 7.62x39. It's plenty capable of taking out larger game. You do however, have to have a 5 round magazine, which is very sensible imo. Don't need people flinging 30 rounds at one deer, it's just not practical. Sporting rifles are good for follow up shots. I know there's a lot of people in the southern united states that use them for hog hunting, because there's so many of them.
To end this: Do I think people should have these for hunting and self defense? Yes! People need to stop using scare tactics and loaded terms and be real. Call them what they are - semi-auto rifles. If you ban "assault weapons" all you'll do is change the cosmetics of the gun. Take new York for example. They have banned "assault weapons" better than any other country or state, and guess what? They still have ar-15's! Just no collapsible butt-stock, bayonet lug(never heard of a mass killing with one of these), neutered magazine capacity, flash hider, pistol grip, and much more. It's ironic because it shoots the exact same round, and mechanically functions just the same.
So let's use common sense, and not ban unicorns.
The Second Amendment of the United States Constitution reads: "A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed." We need guns to protect ourselves and our families from dangerous people or animals.
Assault weapons are ill-suited for civilian use. They are military-style guns capable of rapid fire shooting and can hold a very high number of rounds of ammunition. The same goes for assault rifles, only without the military features such as grenade launchers and bayonets that assault weapons are equipped with. We need to start using common sense and stop listening to rhetoric from the NRA.
First of all, assault weapons are made for military. Which means criminals could be armed and it may increase the risk of terrorism. So I personally think that handguns are dangerous enough. But when civilians own a gun that was intended for military, it won't be good. So weapons that people own should be limited.