I've been hosting my site from home for a few years now.
I use no-ip's DNS service (I don't have a static IP).
It's come time to move to a web host due to slow speeds (expected from DSL really).
When I move to a pro host I'll no longer need no-ip.com attached to my domain name. The problem is that all links to *.no-ip.com in my site and any site that has links to mine, now become broken.
Someone else out there must have experienced a similar situation.
I'm just wondering what's the best way to deal with this.

Your best bet is to point the no-ip.com domain to your new website IP. If your on a shared IP try getting a dedicated or talk to your host and they might be able to setup a virtualhost alias in apache for it.

After three or four months once usage on the old domain fades off you can drop it all together. Another possibility is to continue running a webserver on your IP and just show a page saying "We've Moved'

Thanks. I do have an ip from the new host. that's what I'll try.