Two thoughts come to mind...
PractisePower wrote:
...
The work around seems to be to:
Select the cell
2. Enter the equals sign (=)
3. Type SUM
4. Open brackets (
5. Manually type the range you need e.g. B1:B5
6. Close brackets )
7. Hit enter and your result is in the cell without spilling.
That's a little wordier than needed.
After typing SUM you can press return to accept that function. Numbers automatically enters the parentheses (opening and closing) and selects the parameter field for what to SUM(). You can either type or drag over the cells to mark the range, then press return again.
Beyond that, though, I suggest you're doing it wrong... or at least 'old school' :)
Specifically, to mention:
> I would usually be able to calculate subtotals in rows for each separate category and then have a TOTAL cell that I entered the formula to add them all together.
For that I suggest you look at Numbers' Categorization functions that will do all this in a couple of clicks.
For example, let's say you have this table of names and values and you want to categorize it by person:

in the Inspector -> Organize -> Categories you can tell Numbers how to categorize the data:

Choosing 'Person' results in automatic grouping of the data by person:

To get subtotals of the various categories, click any of the Payment cells alongside any name (e.g. Bob/Payment) and click the gear wheel to get a list of how you want to summarize the categories. Choose Sum:

Done:

Numbers will automatically take care of grouping each row into the respective category. It will add new categories as names are added, and will track the subtotals.
It's also easy to suppress the individual rows by toggling the disclosure triangle alongside each category label (Name, in this case). This makes it trivial to get a summary table with subtotals, without the minutiae of the every row being shown.
Manually laying out this type of form is, for most cases, no longer necessary.
In general, though, spreadsheets have evolved from massive tables of rows and columns, that you have to define to the nth degree. Let it do more of the heavy lifting for you.