Yes, there is. I recommend reading documentation related to Mathematica contexts. In a nutshell, all variables belong to some context (namespace), and all variables can be accessed via their fully-qualified names of the form "ContextName`varName". If you just use "varName", Mathematica will search contexts in
$ContextPath (try evaluating the variable
$ContextPath to see what it is), and will use the first context where it finds that variable. In addition, each notebook specifies a context (stored in the variable
$Context) where all its variables are stored (unless fully-qualified name is used).
By default, for all notebooks the context is "Global`". Also by default, $ContextPath for all notebooks includes the "Global`" context (as well as "System`" and some others). The net result is that variables are shared across notebooks, and this can rather quickly become annoying. However, there's an easy solution. To create a "private" context for a notebook, evaluate the following:
SetOptions[EvaluationNotebook, CellContext -> Notebook]
This notebook will be assigned a unique context (evaluate the variable
$Context to see what it is). Also, global context will be removed from ContextPath (try evaluating
$ContextPath before and after the
SetOptions[...] above to see what's going on.)
[Update: As pointed out by rcollyer on the new Mathematica stack exchange, to set this option as the default for new notebooks, do the following: open the Options Inspector (Ctrl+Shift+O), change the scope (in the dropdown on the top) from "Selection" to "Global Preferences"; on the left expand the nodes Cell Options -> Evaluation Options, and change the CellContext setting to "Notebook."]
Now, here's how to create a shared context:
varShared1 = "Shared string";
Alternatively, you could've just typed
SharedContext`varShared1 = "Shared string";
Now you can either use the fully qualified names ("SharedContext`varShared1" will work in any notebook), or you can add the context to $ContextPath:
If you do this in all notebooks, varShared1 will become visible without a fully-qualified name.
To summarize, context work a lot like many other search paths. However, there are many subtleties (for example, if a symbol has already been defined in some other context, the Begin["SharedContext`"]/End block might not work as you expect -- the existing context of the symbol will be used instead of SharedContext`), so I recommend a healthy dose of experimentation and perusing the docs.