Depends what they're for and how many.
Most companies will hire to you if you have a speeding fine, or traffic light offence. Some may even allow for two such.
Nobody will hire to you if you have anything to do with drinking/drugs and driving, any insurance offences, or any Dangerous/Careless/Reckless driving codes.
If you have been banned, even for topping up, and it's still on your licence, you won't be able to hire either.
It's not the actual companies that make these rules, it's their insurers