Rennetless cheese?!
Answers: what types/brands etc of cheese DO NOT contain rennet??
That depends on whether you are using rennet as a generic term for coagulant, or whether you mean cheese that doesn't utilize an animal based coagulant.
Some of these other answers are a little off. Most true brie contains rennet. The Bocconcini mentioned is actually a size specification of mozzarella (which may or may not contain animal rennet by producer).
The aforementioned ricotta and mascarpone are correct as they utilize recooked whey to produce and don't need coagulant.
Otherwise you can check out the following list of domestic artisan and farmstead dairies for cheeses that use microbial or vegetal coagulants for some or all of their cheeses:
Achadinha Cheese Company - Petaluma, CA
Alsea Acre Goat Cheese - Alsea, OR
Amaltheia Dairy - Belgrade, MT
Appel Farms - Ferndale, WA (veg rennet for all but one, an aged gouda only available on the farm)
Appleton Creamery - Appleton, ME (Organic Veg)
Beecher's Handmade Cheese - Seattle, WA
Beltane Farm - Lebanon, CT
Black Mesa Ranch - Snowflake, AZ
Bodega Goat Cheese - Bodega, CA
Bulger Creek Farm - Notasulga, AL
Bush Meadow - Union, CT (switching to vegetarian rennet)
Calabro Cheese - East Haven, CT
Carlisle Farmstead Cheese - Carlisle, MA
Catapano Dairy - Peconic, NY
Cato Corner - Colchester, CT (Vivace uses Microbial, otherwise Animal)
Cedar Grove Cheese - Plain, WI
Celebrity Dairy - Siler City, NC
Clover Mead Farm - Keeseville, NY (microbial, switching to cert organic microbial)
Coach Farm - Pine Plains, NY
Cobb Hill Cheese - Hartland, VT
County Meadows - Canton, NY
Cowgirl Creamery - Point Reyes Station, CA
Dona Blanca House of Cheese & Dairy - Saint Rose, LA
Drake Family Farms - West Jordan, UT
Elodie Farms - Rougemont, NC (soft {less than 2 months} use synthetic, hard {3+ months} use animal)
Faribault Dairy Company - Faribault, MN
Farmers All Natural Creamery - Wellman, IA
Firefly Farms - Bittinger, MD
Fiore di Nonno - Lincoln, MA
Fiscalini Farmstead Cheese Company - Modesto, CA
Fraga Farm Goat Cheese - Sweet Home, OR
Frog City Cheese - Plymouth Notch, VT
Gillis Acres Farm - Greenwich, NY
Grafton Village Cheese Company - Grafton, VT
Harley Farms Goat Dairy - Pescadero, CA
Haystack Mountain Goat Dairy - Ada, OK
Heamour Farm - Madison, NY
Hillman Farm - Colrain, MA (fresh uses goat or microbial)
Liberty Fields Farm - Saco, ME
Little Falls Farm - Harrison, ME (Have used Animal, Vegetable and Microbial)
Locust Grove Farm - Knoxville, TN
Mauthe's Dairy - Folsom, LA
Meyenberg Goat Milk Products - Turlock, CA
Monroe Cheese Studio - Monroe, ME
Mozzarella Company - Dallas, TX
Neighborly Farms of Vermont - Randolph Center, VT
Nettle Meadow Goat Farm - Warrensburg, NY (organic veg for chevre & fromage blanc, animal for kunik)
Northland Sheep Dairy - Marathon, NY
Painted Goat Farm - New Lisbon, NY (animal w/ special batches for family with microbial)
Pholia Farm - Rogue River, OR
Rockhill Creamery - (only feta made with veg, the rest with calf rennet)
Roth Kase - Monroe, WI
Rustling Wind Creamery - Falls Village, CT
Samish Bay Cheese - Bow, WA
Sandwhich Creamery - North Sandwhich, NH
Seal Cove Farm - Lamoine, ME
Sierra Nevada Cheese Company - Willows, CA
Silvery Moon Creamery - Westbrook, ME (originally used a veg rennet w/ good results, but found organic microbial to use now)
Skyhill Napa Valley Farms - Napa, CA
Sleepygoat Cheese - Pelham, NC
Smith's Country Cheese - Winchendon, MA
South Mountain Creamery - Middletown, MD
Spinning Spider Creamery - Marshall, NC
Split Creek Farm - Anderson, SC
State of Maine Cheese Company - Rockport, ME (Organic Microbial)
Steamboat Island Goat Farm - Olympia, WA
Stoney Acres Sheep Dairy - Competition, MO
Sunset Acres Farm - Brooksville, ME (vegetable for 10 years, haven't tried microbial)
Surfing Goat Dairy - Kula, HI
Sweet Grass Dairy - Thomasville, GA (animal for ga gouda & grn hill, microbial for rest)
Sweetwater Valley Cheese - Philadelphia, TN
Taylor Farm - Londonderry, VT
Three Sisters Farmstead Cheese - Lindsay, CA
Vermont Shepherd/Major Farm - Putney, VT
Via Lactea - Brookfield, NH (calves rennet in one aged cheese, microbial in rest)
Washington State University Creamery - Pullman, WA
West River Creamery - Londonderry, VT
Westfield Farm - Hubbardston, MA
Willamette Valley Cheese Company - Salem, OR (3 diff rennets)
Willow Hill Farm - Milton, VT
I hope this helps!
Soft cheeses like cream cheese and brie.
I don't know if you have a Krogers near you, but their brand of cheese in rennent free.
Nearly all cheeses contain rennet. Including brie, camemert etc. Many now have a rennet that has been created by science, and therefore contains no meat product and is vegetarian safe. It will say on the packet if it is non-animal rennet. Cheeses that do not contain rennet include ricotta, bocconcini and mascarpone. All different textures and flavours. All great. Hope this helps.