If you have been refused a visa in the past, it is recommended that you should always apply for a visa before you travel, because the chances of you being refused entry without a visa are higher now.
As you are now married and are thinking of coming to the UK as a visitor, they will likely look more closely at your situation to make sure that you are a genuine visitor and won't try to stay in the UK illegally to be with your spouse (i.e. having a UK spouse would give you more incentive to try to stay in the UK than if you were just a regular tourist coming to see the sights).
It may well be worth applying for a 'family visitor visa' instead of a regular visitor visa as you now have a family member living in the UK:
http://www.ukba.homeoffice.gov.uk/visas-immigration/visiting/family/requirements/If you still aren't planning to move to the UK, then you can make this clear when you apply for the visa and show that you have a job, home and a life in the US that you must return to.