Fighters only with no magic at high level probably wouldn't happen though. They've been collecting just like every other class. So they may have the magic items to let them withstand a magic attack or to become the super tank the other classes need.
Depends on what edition and what standard of success one is going for.
5E, yes, quite easily. They're excellent warriors, regardless of the subclass.
3.5E, it is much harder. The fighter just doesn't get enough to support what it does and remain competitive with most other classes.
I've read tier guides for 3.5 and 5e out of curiosity. I do not do so to take an overpowered character but rather to avoid a weak character that will struggle to contribute. The tiers are rated one through six with one being best. Tier one is occupied by clerics, Druids and wizards. Fighters are down in Tier 5 and are considered limited one trick ponies. I'm not insulting anyone for playing them. Just know that if you don't multiclass out of the fighter class you are limiting the ability of your character to impact upon the game. This is for 3.5. It's not as bad in 5e.
Edited: Kyrroeth on 28th Feb, 2017 - 4:10pm
The fighter can be a strong tank in most any game if you get the right materials and if you have back up the tank can do some serious damage very quickly at higher levels. I have a high level fighter in a game well he is level 12. He does some interesting damage.
The problem with the fighter in 3.5 is that all they can do really is combat. They can't really contribute much to the social aspect of the game etc. Then In combat you have other classes that just overshadow them and can still do other things outside of combat.
Edited: Kyrroeth on 28th Feb, 2017 - 4:13pm
Indeed, the 3.5 fighter is certainly capable of smacking things. But if that is one's only schtick, one ought to be the best at it, or close to it. Some other classes are not only better at smacking things than a pure fighter, but at doing other stuff too.