I have always believed in giving under the new covenant and have used a tithe as the guideline for the minimum amount for giving.
Kat Kerr (www.revealingheaven.com) has been having visits to heaven since 1996. There has been some controversy about her claims, yet she has some irrefutable proof and many big name ministries have endorsed her as being authentic. I have listened and read to most of what is available about her visits to heaven and I have not been able to find anything that she says, contradictory to scripture. She has written two books called "Revealing Heaven 1" and "Revealing Heaven 2".
The following extract comes from the first cd of her series called the "The Celestial Realm":
It all belongs to him anyway, if you tithe you cannot out give God. And then when you give an offering on top of that, especially when you have need yourself you absolutely overwhelm Him. You bless Him, He will tell all of heaven: "look at them and look at that, look at My precious child, they need things themself and yet they're taking from their own hurt, their need, and giving to others."
It blesses Him. The only thing that blesses Him more is when people get saved on earth. When you pray with people to get saved, when you stand in the gap, His intercessors are His super heroes. And there is a hall of heroes in heaven and a hall of super heroes. The super heroes are the ones who never stopped praying till the day they go home. Their life isn't their own, they've given it to Him.
Hearing this statement about tithing from Kat Kerr has convinced me that the principle of tithing still remains under the new covenant. It obviously does not apply in exactly the same way as it did under the old covenant but the principle still applies.