I wouldn't say NONE. Back before I became a true frequent traveler I would still score frequent upgrades simply by being polite and friendly with the gate agent, front desk attendant, rental car clerk, etc.
If the trip is special for some reason (e.g. celebrating a big anniversary), politely mention it at check-in and ask if they can do anything to get you a better room. The worst that can happen is that they say "no". They may offer to upgrade your room for a certain amount of cash per night (which may or may not be worth it to you), or you may catch them on a good day or with low occupancy where they're happy to help a courteous guest as opposed to the obnoxious pigs they deal with day in/day out who rudely DEMAND special treatment. You know the kind who flash Centurion cards or other forms of "VIP-dom" and expect the red carpet to be rolled out?
Just be nice, like you'd want to be treated if you were working the other side of the check-in desk, and see what happens.
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CO plat, UA prem; Marriott plat, Hyatt plat, Hilton gold, Starwood gold, Fairmont gold; Avis select, Hertz 5-star