FFXIV currencies: what tomestones, scrips, seals and MGP buy and what each unit is worth

Allagan tomestones, scrips, Grand Company seals, MGP and the other currencies are spent at exchange vendors, each offer for a fixed lot of an item. The currency comparison lists every exchange a currency pays for, how many your amount buys and, for items sold on the market board, how many gil each unit of the currency turns into.
Where do I see how much I hold?
Open Character in the main menu, then Currency. Enter that amount in the comparison; every row then shows how many exchanges you can afford and what is left over. An exchange that also takes another item or currency names it under the cost.
How is the value per unit worked out?
For an item sold on the market board, the comparison takes the cheapest current listing of the same quality in your region, multiplies it by the lot size and divides by the currency cost. Rows are ranked by that figure. Items that cannot be sold on the market board, and items with no listing right now, stay in the list without a value; a missing price is never treated as zero. A listing is an asking price, not a guaranteed sale, and the time it was observed is shown beside it.
Which currencies are covered?
Tomestones, crafters' and gatherers' scrips, Grand Company seals, MGP, Wolf Marks, Allied Seals, Centurio Seals, Sacks of Nuts, Bicolor Gemstones, Trophy Crystals, Skybuilders' Scrips and the allied society currencies.
Worked example
You hold 1,000 Purple Crafters' Scrips and want only items you can sell (open this selection). Craftsman's Competence Materia X costs 250 scrips, so you can afford four with none left over. Mastercraft Demimateria costs 800, so you can afford one with 200 left. The materia is worth its lowest listing divided by 250 per scrip, the demimateria its listing divided by 800; whichever is higher comes first, and the row links the Scrip Exchange that sells it.