So, I see white vinegar, brown vinegar, malt vinegar. I even had balsamic vinegar on fish tonight (way too strong).
Is there a difference between vinegars in taste (discernable) and what you should use them for?
I dilute apple cider vinegar with water sometimes to give my hair some volume and shine after the final rinse.
Rice vinegar is necessary if you want to make good hot and sour soup.
There are some folks around here that really know their shit when it comes to vinegar. I’m not one of 'em. I like balsamic vinegar on some dishes, and I can’t really tell the difference between the different qualities. I don’t cook with it because my husband doesn’t like it. My son, however, uses it quite a bit.
My only other comment is that German cooking has a lot of plain ol’ vinegar in it. I picked up a recipe for German meatballs (klepsa??) that my husband likes, but he likes the vinegar to be more of a whisper than an open-handed slap in the face (like his uncle).
Yes, there are taste differences between types of vinegars. As with other foods, though, you may or may not have the palate to appreciate the differences. In addition to being made from different substances (white wine, red wine, rice wine, apple cider, etc.), vinegars may be flavored with herbs, fruit, or other things, and they vary in strength. Rice wine vinegar is generally milder than other western types, and good balsamic is highly concentrated. (REAL balsamic is syrupy and should only be used in tiny drizzled amounts.) Also, as with wine, vinegars can vary between brands and even year to year.
Malt vinegar is great on French fries.
I use white vinegar and hot water to clean my kitchen floor (and my hardwood ones as well).
I have now told you all I know. 
Different vinegars do have different flavors, yes. You might not be able to taste the difference in most of them, but you can definitely smell it.
Essentially, any vinegar begins as an alcohol, wine or juice of some sort, and is rendered into a highly acidic form by bacteria. Malt vinegar began as malt liquor; cider vinegar began as apple cider or applejack; rice vinegar began as rice wine; red wine vinegar … well, you can guess that one. You can get balsamic vinegar, sherry vinegar, and dozens of others.
Because it is a product of bacteria, the quality varies depending on how long it’s been allowed to ferment (that is, how much of the starch has been gobbled up by the bacteria).
In addition to different flavors, vinegars also have different levels of acidity. Some are more pungent than others. I usually have 4 or 5 different kinds in my pantry at any given time. Cider vinegar for barbecue stuff, sherry vinegar for vinaigrette, rice wine vinegar for certain Asian foods, etc. Red Wine vinegar is one of the very versatile types.
This. If you cook at all, you really need a variety of vinegars. Each has different strengths and flavors. Red wine vinegar tends to be my default, but cider is a close second. Luckily, all but basalmic are quite cheap.
Yes. Basically it’s sugar + yeast = alcohol. Alcohol + acetobacter = Vinegar (acetic acid).
The best ways to figure out the differences is, honestly, just to taste the different vinegars. White vinegar tastes pretty neutral: just straight up acetic acid. Cider vinegar has a little appley sweetness to it. Balsamic vinegar tastes sweet and usually fairly obviously of grapes. It’s the fruitiest and most strongly flavored of vinegars I use. The really good stuff is aged in wooden barrels for many years. The cheaper grocery store brands are just aged in stainless steel tanks and don’t have some of the characteristic woody qualities of the more expensive stuff. Usually, you drizzle just a little bit of this stuff over meats, cheese, eggs, even fruit and some desserts (strawberries & balsamic vinegar being popular.)
Here’s how I use my vinegars:
White vinegar - pickling, anywhere I want to add acidity without flavor
Red wine vinegar - salad dressings, marinades
Cheap balsamic vinegar - salad dressings
Good balsamic vinegar - accents for meats, cheeses, sauces
Cider vinegar - coleslaw, barbecue sauces, barbecue mops, pretty much anything to do with pork barbecue
Malt vinegar - French fries and sauces or marinades for beefy dishes
Rice vinegar - A number of Asian dishes
Coconut vinegar - Vindaloo, certain Southeast Asian dishes
White vinegar isn’t a food product; it’s a non-toxic cleaning agent. There’s never a good reason to use plain white vinegar in a recipe.
All vinegars, of course, contain acetic acid, but that’s usually not the reason you use it (with the exception of some baked goods or pickles that need an acid for chemical reasons). The reason you use vinegar is because it’s a vehicle for all sorts of other wonderful, subtle flavors. Which vinegar you use then depends on what subtle flavors you want. Personally, I prefer cider vinegar for most purposes, since I learned to cook from my grandma, and that’s what she mostly used: Whenever I open the bottle, it smells like Grandma’s kitchen, and that’s a Good Thing. For a deli sandwich, though, there’s just no substitute for red wine vinegar, and French fries are great with malt vinegar. Basically, think of any sweet or starchy food with its own flavor, and then take out the sweet or starchy component, and the flavor that’s left is what you get in the corresponding vinegar.
Not necessarily: A lot of “white vinegar” is just acetic acid produced from petrochemicals, and then diluted with water (the label will sometimes say “non-brewed condiment” in this case). That’s not really relevant, though, since as I said, you shouldn’t be using white vinegar in the first place.
Would you object to using a dash of white vinegar to curdle milk when a recipe calls for buttermilk and you don’t have any?
I always associate the smell of white vinegar with dying easter eggs.
I love chili vinegar! Mac’s Chili Parlor on Chicago’s South SIde used to make chili vinegar with white vinegar and tons of red pepper flakes. That’s GOOD STUFF. 
You sprinkle it on … everything! Nice hot & tangy.
Not to mention pepper vinegar. Just the thing to shake on greens.
Eh. I kind of like white vinegar. It’s got a very crisp, clear vinegar flavor.
I’d use lemon juice instead, but that’s me.
I like white vinegar just fine, too. It’s used in plenty of Central and Eastern European dishes, and that’s the vinegar I grew up on with my mom’s cooking.
I poured white vinegar on my patio and it killed the weeds growing in the spaces between the paver stones.
I buy really cheap vinegar to clean the scale from the kettle. It just disolves it.
Thanks for the detailed responses.
It can be used to increase the sanitizing power of bleach, or if you mix them directly you can gas yourself.
The maker of StarSan sanitizer (a very popular sanitizer for home brewers) actually advocates the use of a bleach and vinegar sanitizing solution when used EXACTLY like this:
1 fl oz store brand bleach, no scent added
add five gallons of water
THEN add 1 fl oz distilled white vinegar
The vinegar’s ph kicks up the sanitizing power of this small amount of bleach. Only a 30 second soak is necessary, and with this very diluted mixture, NO RINSING is needed.
Interesting. Maybe I’ll give this a shot. The cost of iodophore is becoming prohibitive, and I seriously oversanitize when I brew. (I have a rinse cycle as well though, so I don’t get the associated off flavors.)