I have some places where implementing some sort of cache might be useful. For example in cases of doing resource lookups based on custom strings, finding names of properties usi
This is a large problem, you need to determine the domain of the problem and apply the correct techniques. For instance, how would you describe the expiration of the objects? Do they become stale over a fixed interval of time? Do they become stale from an external event? How frequently does this happen? Additionally, how many objects do you have? Finally, how much does it cost to generate the object?
The simplest strategy would be to do straight memoization, as you have above. This assumes that objects never expire, and that there are not so many as to run your memory dry and that you think the cost to create these objects warrants the use of a cache to begin with.
The next layer might be to limit the number of objects, and use an implicit expiration policy, such as LRU (least recently used). To do this you'd typically use a doubly linked list in addition to your dictionary, and every time an objects is accessed it is moved to the front of the list. Then, if you need to add a new object, but it is over your limit of total objects, you'd remove from the back of the list.
Next, you might need to enforce explicit expiration, either based on time, or some external stimulus. This would require you to have some sort of expiration event that could be called.
As you can see there is alot of design in caching, so you need to understand your domain and engineer appropriately. You did not provide enough detail for me to discuss specifics, I felt.
P.S. Please consider using Generics when defining your class so that many types of objects can be stored, thus allowing your caching code to be reused.