While a mechanical timepiece will never be as accurate as a battery-operated quartz watch, a spring-powered timepiece can provide excellent accuracy (depending on the quality of the movement, of course).
In general, a high-grade watch will keep time within a few seconds a day. A medium grade watch will vary up to 20 seconds a day. A low-grade watch may lose/gain several minutes a day. Many factors affect the quality of a watch, but the jewel count of a typical American made watch will usually be a good indicator of quality. Higher quality watches tend to have up to 23 jewels, medium 15-17 jewels. A watch with seven jewels is considered average, and anything under seven jewels is typical of a poor timekeeper. (These numbers are for time-only watches. Watches with complications such as calendars and automatic winding will have a higher jewel count)
There are other factors to be considered, including temperature and isochronism (the ability to keep constant time throughout the wind cycle of the mainspring). A watchmaker can make fine adjustments to a higher quality watch, improving these variables.
Accuracy also depends on how the watch is worn (sometimes called a personal error). For example, a watch that is lying on your nightstand will run at a different rate than if you are wearing or carrying it all day. One may note a difference in rate over short periods. This rate variation is often smoothed out over 24 hours as the watch is moved between positions. Here again, the higher quality the watch, the easier it is to adjust for positions. High-grade watches will not vary more than 5 seconds or so between 5 to 6 positions, while the seven jeweled watches can vary up to 1 minute between the stem up and dial-up positions.
And any watch that is not maintained well will lose its accuracy over the years. And of course, as the bearing surfaces wear (worn jewels and pivots, and gear teeth), the accuracy will worsen as the piece ages. However, I have seen high grade watches over 150 years old, still keeping excellent time if they have been maintained well.