OP here again. I had never heard of "umami," but I just googled it. Very interesting. I think that is exactly what I'm trying to pinpoint here. Thank you to all. I definitely agree on the mushrooms. Also roasted peppers, etc. I'm about to head down the umami rabbit hole...

You are wanting umami - the rich flavor - as previously mentioned, try mushrooms (you can take them out after you use them to get flavor (ie in a broth or sauce) if you don't want the actual mushroom in the dish. Liquid smoke, an previously noted, is also great - just a few drops.

I also recommend going to Olio or one of the other stores that sell flavored olive oils and getting a sampler to try.

OP it sounds like you're not so much looking for a meat-free option but one that doesn't involve chopped bacon, beef stock, etc?
Worchestershire, fish sauce, and anchovy paste are all good ways to add some depth to a dish, without adding actual pieces of meat, even though the fish sauce and anchovy paste obviously involve fish (not sure about worchestershire...?) I put one of the three in lots of things - soups, stews, chili, braising liquid, sauces, etc.

But I like those PLUS a bit of meat!

It sounds like you're trying to imitate a meat flavor without using meat. I don't think that meat specifically 'adds a depth of flavor' to food. It's just a particular flavor that you like and are trying to recreate. There are many other strong flavors that have no meat products at all. What about garlic, miso, soy sauce, and chili sauce? Also if you can get to an Indian grocery store, there is tamarind to try.

1) Miso
2) Rind of parmesan cheese

Mushroom stock can be very flavorful, and finely chopped mushrooms in a stew can give a very meaty texture and flavor profile.

OP here. Thanks for all the feedback. To vegetarian PP, I understand what you are saying regarding flavors coming from spices, but meat does bring a depth of flavor that is hard to explain/imitate. The closest match I've found (in terms of depth of flavor, not in the flavor itself) is caramelized onions or maybe a strong cheese. To the PP who asked for specific recipes I'm thinking about, this is more of a general question, but things like bean soup (usually I throw some ham in there); chili (maybe the smoke flavoring or chipotle is the one to try there). I recently made this black bean burger recipes, which was very good -- http://allrecipes.com/recipe/homemade-black-bean-veggie-burgers/. Then I chopped up the burger and put it in tomato sauce as a meatball substitute. It was pretty good, though the "meatballs" did not hold their shape.

I am not going completely meat free, but I do want to cut back and the suggestions offered here will help. Thank you, and keep them coming!

Don't most strong flavors come from non-meat products? Herbs/spices/peppers/fruits/veg, etc.

I don't really understand. I've always thought meat would be very bland without vegetarian items. But I'm a vegetarian, so perhaps I don't know what I'm missing!

Anyway, I think the following foods have strong flavors:
Cilantro
Chili peppers
Tomatoes & sun-dried tomatoes
Apricots
Bay leaves
Onions & scallions
Turmeric
Parmesan cheese
Olives
...

And these are my favorite stock cubes (I get them at Whole Foods):
http://www.amazon.com/Rapunzel-Vegetable-Bouillon-2-97-Ounce-Packages/dp/B001E5DZIY

I like to add Toasted sesame oil and Mirin to add lots of flavor and more complex levels of taste. You can also add flavors that will enchance the umami taste such as roasted tomatoes, roasted mushrooms, fish sauce, hard cheeses,

here is a video on making your own base (does use a very small amount of meat) http://www.youtube.com/watch?v=Ais0utM-YDQ

Better than Bullion http://www.superiortouch.com/retail/products/better-than-bouillon/vegetarian-bases
Goya Sazon http://www.goya.com/english/product_subcategory/condiments/sazon-bouillon

Tomatoes or tomato paste. Garlic. Leeks. Parmesan rinds. Soy sauce. Look up the term "umami" and go from there.

Liquid smoke is vegetarian. Harissa. Roasted red peppers. Sundried tomatoes.

Maybe more helpful if you gave example recipes you were trying to eliminate meat from.

Just keep using the meat in stews...I think it's an excellent way to stretch a tiny bit of meat over lots of food. Other than salt/butter/cream/cheese I don't think you are going to get the depth you are seeking.

At least says this meat-lover at heart.

No. Just do something else instead of substituting veggi in meat based dishes.

I'm trying to cut down on my meat consumption, but one place I have a hard time is in cooking stews, soups and sauces. For them I tend to rely on a little bacon or ham for strong flavoring. I've found that caramelized onions offer a strong flavor that is different from meat (obviously) but still works well in many dishes. Cheese is another option for strong flavoring, though that is not so healthy. Any other recommendations for veggie-based strong flavors? I'm 'not talking about spices, per se, more foods themselves. Thanks.