You can export and backup your Gmail contacts on to your computer by saving them as a CSV file. You can then import or transfer your Gmail contacts to other email service or clients. For example you can refer to this tutorial to transfer VCF contacts to iPhone or transfer VCF contacts to Android phones.
Updated with screenshots and Email client support like Outlook, Apple Mail, iPhone iPad Mail and so on, check the page below:
Export Gmail Contacts
1. Log on your Gmail account from the web interface. Sign in to Gmail with your account ID and password.
2. Click Gmail at the top-left corner of your Gmail page, then choose Contacts.
3. From the More actions drop-down menu, select Export….
4. Choose whether to export all contacts or only one group.
5. Select the format in which you’d like to export your contacts’ information. In this case, we select vCard (VCF) format.
6. Click Export.
7. Choose Save to Disk then click OK.
8. Select a location to save your file, and click OK.