The problem comes when you read that state back, and do something about it. Writing is a red herring - it is true that as long as this is a single word most environments guarantee the write will be atomic, but that doesn't mean that a larger piece of code that includes this fragment is thread-safe. Firstly, presumably your global variable contained a different value to begin with - otherwise if you know it's always the same, why is it a variable? Second, presumably you eventually read this value back again?
The issue is that presumably, you are writing to this bit of shared state for a reason - to signal that something has occurred? This is where it falls down: when you have no locking constructs, there is no implied order of memory accesses at all. It's hard to point to what's wrong here because your example doesn't actually contain the use of the variable, so here's a trivialish example in neutral C-like syntax:
int x = 0, y = 0;
//thread A does:
x = 1;
y = 2;
if (y == 2)
print(x);
//thread B does, at the same time:
if (y == 2)
print(x);
Thread A will always print 1, but it's completely valid for thread B to print 0. The order of operations in thread A is only required to be observable from code executing in thread A - thread B is allowed to see any combination of the state. The writes to x and y may not actually happen in order.
This can happen even on single-processor systems, where most people do not expect this kind of reordering - your compiler may reorder it for you. On SMP even if the compiler doesn't reorder things, the memory writes may be reordered between the caches of the separate processors.
If that doesn't seem to answer it for you, include more detail of your example in the question. Without the use of the variable it's impossible to definitively say whether such a usage is safe or not.