Arkham Horror: Tokens
What I do in my playing is give the players enough stamina and sanity tokens to reach their maximum, in denominations so that the player can "break" their stamina and sanity totals without ever having to put them back into the pool, or take new ones out (unless their maximum goes up, obviously).

For example, if an investigator has a maximum of 5 sanity, I'll give them one 3 sanity token, and two 1 sanity tokens, for a total of five.  If they take two points of sanity damage, they move their two single sanity tokens off of their investigator card (or onto their card, it doesn't really matter so long as they are consistent in how they do it).  If they then take a further point of sanity damage, they move the 3 sanity token onto the card, and put the two singles back.

The same can obviously be done with stamina.

There are no official rules that state that something happens when clues or money or explored tokens run out, so I would assume that it's safe to go ahead and replace those with stand-ins (small change works well for money: pennies for $1, nickels for $5, and dimes for $10, for example).

One thing that may be worth checking out if you have an iOS device is the Arkham Horror Toolkit released by Fantasy Flight Games on the App Store.  It can keep track of your sanity, stamina, money and clues.  It's not free, but it does have some other neat features (support for the expansions -also not free, but not too expensive), and a built in dice roller.