I used to spend my summers on our family's farm when I was a kid. We had pigs, chickens, roosters, ducks, turkeys, cats and dogs, some of which would all just roam around freely on the property.
One morning I had just gotten done helping my aunt feed all the animals. It was getting really hot so I went inside to cool off and get something to drink. That's when I noticed my grandpa's cats. I rarely ever saw them as they were usually asleep in the barn or off hunting somewhere, but this time, they had all converged in the kitchen, meowing quite loudly, backs arched, hair standing on end, rubbing up on my grandpa's legs as he was trying to sweep the floor. I had never seen them act like that before, but then again cats can be weird and I didn't really think much of it.
As I sat down at the table, I hear my aunt start hollering outside. I look out the window and see her surrounded by a mob of 25-30 ducks, clamoring and flapping their wings as she was trying to hang the laundry.
I go outside to help her shoo them away and see what's going on. The feeling I got as soon as I walked outside was creepy; the air had this strange feeling to it. I noticed there were no bird sounds coming from the trees; they had all flown away. The pigs were stirring in their pens; I could see the hens in their coops, flapping their wings, feathers ruffled. Our dogs, who were usually pretty calm and docile, were jumping up onto my cousin, not like an untrained dog or puppy might, but almost frantically, like a scared child wanting to be carried, looking for protection.
And that's when it hit. A big earthquake, 8.3 magnitude if I remember correctly. I'd experienced small tremors before, but I had never experienced anything like this. I could see the ground rolling, like waves do in the ocean. It lasted about 10-15 seconds, but those were the longest seconds of my little 10 year old life.
The animals started behaving strangely about a full minute before the earthquake hit.
TL;DR - if you see animals being unusally clingy or acting anxiously, an earthquake may be coming.