Cats are often mysterious and confusing creatures, and what makes things harder is not being able to talk to them using words. Thankfully, cats express their moods and emotions through various key body parts -- think the ears and tail. Tabby cats are certainly no exception to this rule.
If you notice that your precious tabby's ears are totally flat, then he could be pretty annoyed with someone or something at the moment. Maybe you're petting him too much and he's feeling overstimulated and wants it to end. He might see the birds through the window and want to go outdoors to chase after them. Whatever the case is, something may be irking your little one and he wants it to stop -- pronto.
In some instances, when Tabby's ears go down, it could indicate pure belligerence -- yikes. Your tabby cat is likely very upset about something, and may be feeling kind of aggressive about it. Exercise caution around any angry cat. Leave him alone for a while so he can cool off. Avoid petting him or picking him up for a while. If you provoke him, you could end up with a cat scratch or bite, so be very careful and respect the cat's wishes. Feline scratches and bites can be dangerous and lead to infection in some cases.
Flattened ears on a tabby cat can also point to fear and defensiveness. Maybe you're taking your precious pet to the veterinarian to get neutered and he's absolutely terrified by being in the unfamiliar moving car. Perhaps he can spot the neighbor's massive Saint Bernard through the window and he's worried that he might get attacked -- poor thing.
At the total opposite end of the spectrum, ears that are down but pointing out sideways can also be a friendly greeting of sorts. If your tabby meets you at the door the second you get home from work in the evening, his ears placed in this position may just be a way of communicating to you, "Oh, you're back now? Hi! How have you been? Good to see you."