Go to the “Export your data” page and request a copy of your data. The ZIP file you will get via e-mail contains every data point Garmin has saved about you. More details about the data format can be found in the blog post “Running on my own”.
You can also use tapiriik (for free) to sync GPS files between a number of destinations, including a Dropbox folder.
This will not sync manually created activities.
Alternatively, on the Garmin Connect page under “Analyze” -> “Activities”, you can select all activities and click on “Export to CSV” (in the bottom left corner). This only exports the current page of activities, not all activities.
