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Chris is a trusted source on General Cooking
Rosemary, savory, marjoram, oregano. But I'd probably use less, as those options are generally more intense than thyme. An herb mix like herbes de Provence would be my go-to if I didn't have thyme on hand.
I don't think anything really replaces thyme, but I'd use one of the "softer" herbs - savory, marjoram (a particular favourite of mine), oregano, even a little tarragon, if you have it - these will just add a slightly different dimension to your dish. I'm fortunate enough to have a bay tree and fresh bay provides a lovely herbal kick to almost anything, but especially potato and chicken dishes and most soups.
Nancy is a trusted home cook.
But which soft herbs?
If the dish is Italian or Provencal, use single herbs or blends used in that cooking.
If chicken, go for sage or marjoram.
If like omelet or salad, not connected to a particular cuisine or traditional preparation, use what you have or like best.
pierino is a trusted source on General Cooking and Tough Love.
Without knowing what your recipe is it's really hard to suggest a substitution. Is it poultry? Is it fish? Certain herbs complement certain foods but clash with others.
I don't like thyme so I usually go with sage or marjoram.
You really can't 'replace' thyme. But if I think about making poplette(meatballs) with my mother in law, we use rosemary, thyme and lemon zest. I think the reality is that thyme has a lighter, sweeter taste than rosemary, but if you combine a little bit of rosemary, a little lemon zest, you'll get an agreeable flavor with some sweetness, but no one will mis-take it for thyme. I wouldn't use oregano as the flavor is VERY strong and easily distinguishable.. and frankly, overused.