What is the difference in the meaning between the following two tenses?
I used to travel alone.
I was used to traveling alone.
"I used to [do X]" indicates an activity that you have previously performed regularly, but no longer do.
"I was used to [doing X]" indicates that you were accustomed to engaging in a particular activity.
Used to describes an action or state of affairs that was done repeatedly or existed for a period in the past; to be used to (or to get used to) means "be or become familiar with someone or something through experience".
Both the phrases imply that an action has been done repeatedly; they are not used to refer to actions that happened only once.
The NOAD reports the following notes about used to that could interest you.
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