Never rodents, but have had squirrels in the past.
Woke up one very hot morning ( mesh door only closed) to see three squirrels trying to prise open a plastic container in the porch. Not sure who was most surprised. They just froze and stared at me before running off with an empty biscuit wrapper.
I've never seen a rat on a campsite, but have had plenty of encounters with tiny field mice. In Snowdonia we've had the odd one in the tent - had a hell of a time encouraging it out again.
We've also had field mice under the groundsheet, both in Wales & France. In France I had several disturbed nights with them partying away under the groundsheet. I kept thumping the floor to discourage them, but it just seemed to perk them up...
Mouse climbing the flyscreen inside the porch of my Montana in France one year, the dog alerted me to it then scared it off.
Last year we were packing up and a mouse ran from under our ZIG to the nearest bush. I was worried it had chewed but everything was fine. When we moved DS's tent his footprint had been gnawed at, hole right in the middle of it. SIG ok, just footprint chewed.
I'm not very brave about encounters either, but would never sell up.