The vast majority of jobs can only ask for a basic check. Unlock has details of those that qualify for a standard or enhanced DBS. Any business undertaking a standard/enhanced check when the job is not on the prescribed list of exceptions is breaking the law.
Unfortunately there are grey areas and i'm sure there are employers who interpret the regulations for their own benefit and ask for a check which should not really be applicable for the role in question - while there are meant to be checks and balances in the system there is enough anecdotal evidence that these are rigorously enforced.
Having said all of that, to reiterate the first point - the vast majority of employers play by the rules and if you can provide a clear basic DBS you will find there will be lots of opportunity out there.
Obviously, steer clear of any role that involves interaction with children or vulnerable adults, and if you have dishonesty convictions I would steer clear of anything related to financial services. Beyond that, hopefully the world is your oyster as the saying goes...