In many cases, you want to test whether or not items are cursed. Here are a bunch of ways to do that, though this list is likely incomplete.
Ways that work on most items
These methods work for all classes of object.
Items dropped on an altar will glow black if cursed. You must not be blind to use this technique. (Blessed items will flash amber.) This is a common method later in the game; even in Gehennom you can use the altar in Orcus-town. Sometimes you want to figure out cursed status before you can get to an altar; other methods can help with that. Note that if you are hallucinating when you do this, this method will only identify those items that are uncursed, as you will be unable to tell the difference between a black and an amber flash while hallucinating. Altar testing breaks atheist conduct unless blind.
A pet will "move only reluctantly" over any stack of objects that contains one or more cursed objects, as long as the pet was not whistled onto the stack (using a magic whistle) and the stack contains no food. Pets will greedily eat up food of their preferred types without regard to cursed items underneath or above the food.
Reading a scroll of identify (or casting the spell, or getting the gift from a throne) will reveal the cursed status of any items identified. If you can cast identify at low failure rates and want to know the status of something now, this can actually be very useful.
Holy or unholy water
If you are willing to use up holy or unholy water, you can determine whether or not an object is cursed. If you think the object might be cursed and are OK with it becoming cursed if it isn't, dip it in unholy water. If nothing happens, the item was already cursed. If you think the object might be cursed and you want it uncursed, you can dip it in holy water, and it will uncurse itself if cursed and bless itself if uncursed. If the item was already blessed, nothing will happen. This technique can be useful with items that don't stack and are expected to be either cursed or blessed.
You can dip items in a fountain and may find out whether or not they are cursed. There is a 4/30 chance that the item will become uncursed if cursed ("The water glows for a moment") or, if already non-cursed, nothing will happen ("A feeling of loss comes over you"). However, there is also a 1/30 chance that the item will be cursed outright with no message. Before choosing to employ this strategy, you should go read about the other potential effects of dipping in fountains and be sure that you don't mind the other effects.
Methods that work on weapons
Wield the item
If the object you want to identify is a weapon, wield it and try to unwield it. If you can, it wasn't cursed. This method has the problem that, if it was cursed, your hands are now welded to the object. This is fine if you have a scroll of remove curse you were looking to burn or can cast remove curse at low failure rates — as long as the object wasn't a two-handed weapon.
Try to make a monster wield it
Drop the weapon in front of a monster that will pick it up and wield it. If the weapon "welds itself to the monster's hands" or something similar, it's cursed.
Cursed projectile weapons like darts, daggers, or shuriken may sometimes veer wildly off in another direction if you or a monster tries to throw them. They will not weld to your hands if you do this. You can #name a cursed projectile and other cursed projectiles of the same enchantment will stack with it, allowing you to detect further cursed items.