Even though the question seems trivial, it's still a hotly debated topic (as far as I'm aware). For example, in the Oxford Handbook for Polysynthesis, Fernando Zúñiga says:
Recent literature (e.g. Dixon and Aikhenvald 2002b) has emphasized the need to distinguish, in principle, between low-level units identified via phonological and prosodic rules (p-words) and those identified via rules of grammar (g-words).
Is this a meaningful distinction? What other distinctions are there? What languages present problems when the concept of word is introduced to them?