HttpContext.Cache Expiration

You can specify it in the 4th parameter of Cache.Add():

public Object Add(
    string key,
    Object value,
    CacheDependency dependencies,
    DateTime absoluteExpiration,  // After this DateTime, it will be removed from the cache
    TimeSpan slidingExpiration,
    CacheItemPriority priority,
    CacheItemRemovedCallback onRemoveCallback
)

Edit:

If you access the cache via the indexer (i.e. Cache["Key"]), the method that is called uses no expiration and remains in the cache indefinitely.

Here is the code that is called when you use the indexer:

public void Insert(string key, object value)
{
    this._cacheInternal.DoInsert(true, key, value, null, NoAbsoluteExpiration, NoSlidingExpiration, CacheItemPriority.Normal, null, true);
}