We'll address specific gown styles and material and the recommended lingerie for them. Before we do, Eve's Apples would like to thank Bedtime Flirt for offering information and quotes on this post.
Strapless: The last thing you want to do with a strapless gown is go without a bra! It's highly recommended to go with "bridal corset or lace bustier." Both will give the greatest support.
Strapless with Crepe or Chiffon: This material is most likely too lightweight to wear a corset. It's recommended to go with a strapless bra (in a soft, comfortable material like microfiber) without embellishment to maintain a sleek look on the outside. Bedtime Flirt specifically recommends "underwire cups that sit flush against the ribs and strong elastic across the top."
Either the Bridal Bustier (with removable straps) and Donna Karan strapless bra (without seams and with underwire) below will work on the above images. Note that this strapless bra is also excellent for sheath and bias-cut gowns since it is seamless.
Empire Waist: An empire waist did a lot for Josephine and is complimentary and comfortable on many figures. Since the waist hits under the bust, you can play a little more with lingerie options. You can go with the standard strapless bra, corset, or bustier. Your other fun option is to have a teddy with underwires. Lace is also an option with this style and a heavier material like satin. 
Empire Waist with Crepe or Chiffon: The above recommendations on Empire Waist work here too. However, you'll want to look at the cut of the dress and how the material falls next to the body to see if you can wear lace lingerie or not. 
Sheath & Bias-Cut: Both of these styles "cling to the body" and require a seamless bra set or body piece in a nude color--whatever is closest to your skin tone. The objective is to give you support and look like you aren't wearing anything underneath. A thong or Commando panty (in buck naked) is the best to pull off this look.
Halter: Choose a strapless bra or a convertible bra. If the gown is low in the back, you can use backless bras that adhere to your breasts at the sides for support.
Low Necklines & Backless: These popular styles require more function than fashion up top. Lingerie tape or a backless bra that adhere to your skin are good options. "For a truly plunging backline you can use a bra adjuster so that your straps wrap over the shoulder then around the waist."
Sheath & Bias-Cut: Both of these styles "cling to the body" and require a seamless bra set or body piece in a nude color--whatever is closest to your skin tone. The objective is to give you support and look like you aren't wearing anything underneath. A thong or Commando panty (in buck naked) is the best to pull off this look.
Halter: Choose a strapless bra or a convertible bra. If the gown is low in the back, you can use backless bras that adhere to your breasts at the sides for support.
Low Necklines & Backless: These popular styles require more function than fashion up top. Lingerie tape or a backless bra that adhere to your skin are good options. "For a truly plunging backline you can use a bra adjuster so that your straps wrap over the shoulder then around the waist."
Panties & Heavy Bridal Material: You can wear thongs, bikinis, briefs, boy shorts, tap pants, tanga and lace. Your only limited by your imagination as long as it doesn't create rogue lines under your gown.
Panties & Delicate Material: This material, like chiffon, georgette, silk, and crepe is going to show lines, especially if the cut of the gown is close to the body. In this case, it's recommended to wear a seamless thong or Commando panty.
Tip for D Cup+: Bedtime Flirt recommends that you "have the dress fitter tack the bra inside the dress to keep lift at maximum height. If your your happy to go braless but still want to keep your modesty intact use lingerie tape a favourite amongst celebrities for those red carpet moments."
Tip for AA & A cups: Look for strapless or convertible bras with silicon, air or water inserts. This will boost up your breasts and create cleavage.
No matter what you choose to wear underneath your bridal gown, make sure that you're comfortable and feel good about yourself! That's one of the best ways to ensure you enjoy your day and Celebrate Your Inner Eve!
