If you are dealing with a street vendor, for example the street market of San Lorenzo in Florence, asking for a discount is expected, especially if you buy multiple items. For example if you buy 3 leather belts, a purse, and a wallet, from the same street vendor you are likely to get some discount if you ask. Therefore it pays to buy several items from the same vendor rather than the same separately from multiple vendors (all those trinkets are made by the same Chinese owned companies in Tuscany anyway, so they are all the same).
At a regular store, it’s like in the US, not much of a negotiation. However it doesn’t hurt to ask for a discount, especially for multiple items purchased or for large purchases. At most you get a “no, sorry!”. Sometimes the store owner has some discretion. Also pull out your credit card, then ask if there is a discount for using cash. I have friends who own shops in Florence, who will give you 5% to 10% discount over the listed price if you pay cash. Those discounts for using cash instead of credit card would be illegal in many US states, but they are common in Italy.