I used to have AEROFORO.COM hosted at one VPS and recently migrated to another provider. I also changed the NS to the new VPS nameservers.
The problem is that now my site hops back and forth between VPSs. Sometimes it loads the old one (closed) and sometimes it loads the new one.
The weird part is that when I ping the domain, I get the new IP address. However, the browser loads the old IP address...
What could be causing this?

I could really use help with this one as it is still happening and it has been over 36 hours since I changed the DNS on the domain.

If you put the domain intodns.com do DNS still point to the old and new VPS?

Yep, this is exactly where I want to be:
Your www.aeroforo.com A record is:
www.aeroforo.com -> aeroforo.com -> [ 69.10.59.157 ]
If I ping using the command prompt, I get the correct address:
C:\Users\Daiver>ping aeroforo.com
Pinging aeroforo.com [69.10.59.157] with 32 bytes of data:
Reply from 69.10.59.157: bytes=32 time=149ms TTL=52
Reply from 69.10.59.157: bytes=32 time=149ms TTL=52
Reply from 69.10.59.157: bytes=32 time=153ms TTL=52
Reply from 69.10.59.157: bytes=32 time=630ms TTL=52
Ping statistics for 69.10.59.157:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 149ms, Maximum = 630ms, Average = 270ms
However, all browsers load the old version. It is so weird. :S

Is your ISP using a cache proxy ? or do you have proxy settings in your browser?
It certainly shouldnt hop! :| On the VPS if it is running a controlpanel, is its local DNS setup for the new IP address?
IE when you moved it, you changed ALL old IP addresses within the VPS to the NEW IP addresses, including the DNS ones?
What if you send an email to your site, do you recieve it on your old or new VPS, or not at all ? Make sure you set that you want delivery verification so that if it bounces, you know where it bounces from.

Nope.
I deleted the DNS Zones in the old server and how it seems to be working.
The question is why if the DNS were changed on the domain were they still hopping back and forth?

Because it can take as much as 72 hours to fully propagate throughout the internet.

However, once it has shown the new IP address, why would it go back to the old one? Is that normal propagation behavior?

However, once it has shown the new IP address, why would it go back to the old one? Is that normal propagation behavior?
No, but it is normal real world behaviour.
The cause is found in certain earlier versions of BIND. These versions, in a misguided attempt to improve performance, did not *ever* go back to the root servers looking for a new NS *unless* they could not get an answer from the NS at the address in their cache.
This is a behaviour that is specific to BIND, and those particular versions of BIND.
Anyone not believing this can go check the release notes from the authors of BIND at isc.org.

No, but it is normal real world behaviour.
The cause is found in certain earlier versions of BIND. These versions, in a misguided attempt to improve performance, did not *ever* go back to the root servers looking for a new NS *unless* they could not get an answer from the NS at the address in their cache.
This is a behaviour that is specific to BIND, and those particular versions of BIND.
Anyone not believing this can go check the release notes from the authors of BIND at isc.org.
This was a confirmed issue with older versions of BIND however these have since been corrected. It's also like pointed out, real world behavior. DNS propagation can be a nasty process, and can take up-words of 72 hours to fully complete (sometimes even longer if you're behind a nasty DNS cache). It will happen eventually, just plan accordingly. On the other hand, maybe I'm lucky... on personal web sites, it has only taken myself near 20 minutes to see reflected changes. Maybe my ISP rocks? :)