Great question. It has been a longstanding issue on Google that it defaults to 'last touch attribution', meaning the conversion is attributed to the last channel a visitor arrives from.
In the new version of Google Analytics, Google introduced Multi-Channel Funnels, to show you "how your marketing channels (i.e. sources of traffic to your website) work together to create sales and conversions."
In the reports, channels are credited according to the roles they play in conversions-- how often they assisted and/or completed sales and conversions. The Assisted Conversions report shows how many sales and conversions each channel initiated, assisted and completed, and the value of those conversions and sales.
The Top Conversion Paths report shows the conversion paths that your customers took on their way to purchase. Time Lag and Path Length reports show how long (in days and in interactions) it took for visitors to ultimately become customers.
You can read the full documentation on Multi-Channel Funnels here:
There is also a good overview video on the GoogleAnalytics Youtube channel here:
To access the new version of GA, log into your account. You should see a link in the top nav bar named 'New Version'.
If you don't see the new version link, you might need to opt-in for it here:
Update: Multi-channel funnels are now available for all users of Google Analytics: