As others have mentioned, perhaps this is not something that academic linguists care too much about. But it is certainly true that some languages borrow more than others, and it can be quite fun for language learners to identify the "borrowing patterns" in various languages.
Here is a rough listing of "heavy", "moderate", and non-borrowing languages.
(languages in bold are those that I know personally. Examples that I'm not too sure about are marked with ?, please feel comment if you know these languages)
Examples of heavy borrowing languages:
Examples of moderately borrowing languages:
- Many other western European languages e.g. Spanish, French, German
- Some/most Indian languages? (borrowings from Sanskrit/Persian/Arabic)
Examples of non-borrowing languages:
- Ancient languages like Latin and ancient Greek. (edit: not really true, probably belongs to the category above)
English is certainly a heavy-borrowing language, with much of its vocabulary derived from Latin and French. Languages of the Sinosphere (Japanese, Korean, Vietnamese) show a similar pattern with borrowings from Chinese. Japanese is particularly interesting in its historical similarity to English: both are island languages that borrowed significantly from its more civilized continental neighbor. There are many native-Japanese/Sino-Japanese word pairs, just like the many Germanic/Latin pairs in English. Maybe other languages also fit this model (e.g. middle eastern languages borrowing from Arabic, South/SE Asian languages borrowing from Sanskrit) though I am not too familiar personally.
Next are "moderately" borrowing languages; most European languages (other than English) probably fit in this category, with various borrowings from Latin, Greek, (more recently) English, etc.
(Note that even Romance languages can have "borrowings" from Latin in the form of more advanced and scientific vocabulary that was coined directly from Latin in Renaissance or early Modern times.)
Lastly, there are those strictly non-borrowing languages. The only one I am familiar with is Chinese, which doesn't allow loanwords due to the cumbersome nature of phonetically transcription in its writing system. Also, ancient languages generally fall into this category, for obvious reasons (though Latin might actually be a borrowing language, due to its borrowings from Greek)