There are two basic categories of mining claims, Patented and Unpatented. The most common type of these is the unpatented claim.
Here is a partial list of activities that are specifically prohibited on an unpatented mining claim (lode or placer):
HOBBY or CURIO SHOPS, CAFES, TOURIST STANDS (These are all "no-nos" in terms of how your claim can be used.)
NON-MINING RELATED HABITATION (You can't use your claim as land to live on, build a residence or vacation cabin, and so on. Any structures erected have to be associated directly with your mining activites and these are usually MINIMAL for a placer mine operation. However, you can camp out or be "in residency" on a public lands claim for up to 14 continous days over any 90-day period.)
CULTIVATION (Your claim can't be used to grow crops of any sort, legal or otherwise.)
ANIMAL MAINTENANCE or PASTURAGE (No, you can't use your claim as a cattle range, grazing area or as horse stables, and so on.)
SMALL TRADE OR MANUFACTURING CONCERNS (Your claim can't be used as a location for small business or manufacturing.)
WASTE DISPOSAL/RECYCLING (No, you can't use your claim as a dumping ground for trash, old cars and equipment, or toxic wastes. Additionally, your claim cannot be used as a recycling center for other people's waste.)
SEARCHING FOR BURIED TREASURE, TREASURE TROVE, or ARCHAEOLOGICAL SPECIMENS (Interestingly enough, you cannot search for buried treasure or treasure trove on your claim. Nor can you use it to loot archaelogical sites or recover artifacts. Your claim is strictly for mining, nothing else.)
HUNTING or FISHING CAMPS (You cannot use your claim as a hunting or fishing camp, or any other related "pay-as-you-go" enterprise.)
TIMBER or VEGETATION REMOVAL (You cannot remove trees or vegetation from your claim unless necessary for conducting mining operations.)
As an unpatented claim holder,you DO have the right to prevent others from trespassing on your claim to prospect or mine.
You CANNOT, however, prevent others from crossing your claim to engage in lawful recreational activities, provided those activities don't interfere with your mining operations.
(For example, if a fisherman casts flies for trout upstream from where you have your dredge running, you can only wave hello at him and go about the business at hand.)