A safe is one of the most common types of safe-keeping storage hotels can offer. Most hotels, from low end to high end, can provide an in-room safe to store your traveler's checks, jewelry and travel documents. Many in-room safes allow you to choose your own password to get in and out of the safe, ensuring that no one else has access to opening that lock. If your room doesn't have a private safe, the hotel most likely has a main safe that they can store your items in during your stay.
Many luxury hotels and resorts allow guests the option of storing precious items with the concierge. These items are checked in and meticulously documented, and held behind the concierge desk in a protected area. This protects you from theft in the case that your room is broken into or if you fear thievery from the housekeeping staff. This is a popular practice for storing passports. Many hotels will hold guests' passports so each guest can rest easy and not fear they will lose their passport during their vacation.
Lockers are a common way of storing items, and some hotels will have lockers available to their guests. This is very common in pool or spa areas of the hotel, allowing guests to store their clothes, shoes and cell phones while they swim or receive a massage. Locker storage is also popular at motels or hostels, where guests have less room in their living quarters and need extra space to store their luggage or larger items.