Given the buffering inherent in all the stdio functions, I would be tempted to read the stream character by character with getc(). A simple finite state machine can identify word boundaries, and line boundaries if needed. An advantage is the complete lack of buffers to overflow, aside from whatever buffer you collect the current word in if your further processing requires it.
You might want to do a quick benchmark comparing the time required to read a large file completely with getc() vs. fgets()...
If an outside constraint requires that the file really be read a line at a time (for instance, if you need to handle line-oriented input from a tty) then fgets() probably is your friend as other answers point out, but even then the getc() approach may be acceptable as long as the input stream is running in line-buffered mode which is common for stdin if stdin is on a tty.
Edit: To have control over the buffer on the input stream, you might need to call setbuf() or setvbuf() to force it to a buffered mode. If the input stream ends up unbuffered, then using an explicit buffer of some form will always be faster than getc() on a raw stream.
Best performance would probably use a buffer related to your disk I/O, at least two disk blocks in size and probably a lot more than that. Often, even that performance can be beat by arranging the input to be a memory mapped file and relying on the kernel's paging to read and fill the buffer as you process the file as if it were one giant string.
Regardless of the choice, if performance is going to matter then you will want to benchmark several approaches and pick the one that works best in your platform. And even then, the simplest expression of your problem may still be the best overall answer if it gets written, debugged and used.