Best practice for using assert?

Is there a performance or code maintenance issue with using assert as part of the standard code instead of using it just for debugging purposes?

Is

assert x >= 0, 'x is less than zero'

better or worse than

if x < 0:    raise Exception('x is less than zero')

Also, is there any way to set a business rule like if x < 0 raise error that is always checked without the try/except/finally so, if at anytime throughout the code x is less than 0 an error is raised, like if you set assert x < 0 at the start of a function, anywhere within the function where x becomes less then 0 an exception is raised?