If you are using Wi-Fi on an iPhone, do certain tasks use your data plan still?

I know using Wi-Fi is very efficient to slow down your data plan usage, but does it completely eliminate using data out of a monthly data plan on phones or does it just cover part of your everyday tasks? Say I was on Wi-Fi and watched videos all the time, downloaded apps all the time, etc. And I was also under Verizon 4g. Would the Wi-Fi completely cover all of that browsing and usage or would any of the data "leak" from my data plan?

When using Wi-Fi the phone will rely completely on the Wi-Fi. The only exception would be certain security tasks. Just as an example, I have a DROID phone with Verizon. Up until the last update, the "My Verizon" app would only use plan data. Apple may have similar apps. But for the sake of, let's say video, streaming netflix for 8 hours while connected to Wi-Fi will ONLY use the Wi-Fi. BUT, if that Wi-Fi disconnects without your knowledge (like if your phone gets Wi-Fi in one part of the house but not another, and you move to the "dark side" of the house) it will seamlessly switch to plan data. Hope that helps you out.

When connected to Wi-Fi on an iPhone, the 4g service is not used at all

Once connected to Wi-Fi, it will only use the Wi-Fi connection. To make sure you don't "leak" your data plan in the event the Wi-Fi goes down, just make sure the Cellular Data on the settings is turned off when not in use.

Wi-Fi takes precedence over any other connectivity mechanism for internet. When you are connected to Wi-Fi all your other internet connections are temporarily suspended. If you were under Wi-Fi coverage all the time then you would not incur any charges on your Verizon 4G plan.

However not everywhere you go may have Wi-Fi, i.e. If you have Wi-Fi at home and you go out and there's some app syncing data with the internet, then it would connect to your 4G plan.

As a rule remember, there's no task that specifically requires you to connect to 4G if Wi-Fi is available. If you always have Wi-Fi available, it would cover All of your everyday tasks.