It started today, I have black pixels flickering on the screen. What is it? and How can I fit it?

1) be sure it's not your tv - do they appear with another device or with tv signal? 
2) maybe the cable is loose, or busted? make sure it's plugged in tight. if so, maybe borrow another cable from a friend to see if that fixes it. 
3) try plugging the wii into a different input on the same tv, this will test that specific input on the tv... 

Try the Wii on another TV. If the problem persists, try another set of cables.

" 1) be sure it's not your tv - do they appear with another device or with tv signal? 2) maybe the cable is loose, or busted? make sure it's plugged in tight. if so, maybe borrow another cable from a friend to see if that fixes it. 3) try plugging the wii into a different input on the same tv, this will test that specific input on the tv...  "

" @Meptron:@Meptron said:

" 1) be sure it's not your tv - do they appear with another device or with tv signal? 2) maybe the cable is loose, or busted? make sure it's plugged in tight. if so, maybe borrow another cable from a friend to see if that fixes it. 3) try plugging the wii into a different input on the same tv, this will test that specific input on the tv...  "

This is an example of what is going on...
 

"

Sounds like your Wii's GPU is about to die. If all else fails, call Nintendo & send it in, they should fix it for free even outside warranty with enough whining about how it's their fault the unit was defective and it has nothing to do with misuse and what not.

I got this problem with my first wii (from launch) and I read somewhere that it was WiiConnect24 that caused the wlan chip to somehow overheat the gpu since the fan is not running when in WC24 mode.  

My wii was out of warranty. But because it was less than 3 years old, I was able to RMA it since it was a design flaw and not abuse on my part. Got a brand new system with my old settings and Miis on it for free except the cost to send it in. It took pretty much exactly two weeks if I remember correctly. This was in Sweden where Bergsala AB is the local distributer of Nintendo stuff but there's probably not much of a difference when it comes to manufacturing faults. 
 
Oh and I haven't used the WC24 mode on the new console in fear of it happening again. Still works fine :>

" I got this problem with my first wii (from launch) and I read somewhere that it was WiiConnect24 that caused the wlan chip to somehow overheat the gpu since the fan is not running when in WC24 mode.  My wii was out of warranty. But because it was less than 3 years old, I was able to RMA it since it was a design flaw and not abuse on my part. Got a brand new system with my old settings and Miis on it for free except the cost to send it in. It took pretty much exactly two weeks if I remember correctly. This was in Sweden where Bergsala AB is the local distributer of Nintendo stuff but there's probably not much of a difference when it comes to manufacturing faults.  Oh and I haven't used the WC24 mode on the new console in fear of it happening again. Still works fine :> "

All the possible outcomes have been suggested here, but I'll still say it for fun:
 
1. Maybe it's your TV settings.
 
2. Maybe it's the cables, getting damaged for bad treatment or being pulled and such.
 
3. Maybe it's the Wii GPU having a problem, maybe from having it overheat by bad placement/overuse/modifying it and such.

I called Nintendo and they said it will cost me $75 to fix because it is out of warranty. Should I do it? Or buy a new Wii?

Did you try to push them, many people are able to get a free repair outside warranty with the right (but usually polite) words.

If not, it sounds like the repair is your best option, in order to both not pay full price and keep all your WiiWare/VC games (otherwise you'd have to once again contact Nintendo, tell them the problem, etc, and send both Wiis in for them to do the licences transfer and wipe your first Wii or whatever).