The verb "to travel" does not necessarily need the preposition "to".
1) I have travelled a lot.
2) I travelled when I was young.
The preposition "to", however, reinforces the idea of going from one place to another. So I would say both examples are correct though the form with "to" is perhaps more usual.
You can also travel "in" a country or "around" a country.
In your final example a proposition is necessary but it does not have to be "to":
What countries have you travelled to? ~ simply means which countries have you visited.
What countries have you travelled around? ~ means which countries have you not only "visited" but also "explored".
But even here I don't think the difference is critical.
P.S. In British English the final "l" is doubled in the past.
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