Here's the information by bootgod. First the pictures:
The tool:
How to open:
Explanation by Bootgod:
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2 tools used: quik-grip clamp and wide blade screwdriver, I've filed mine done to be as thin as possible at the tip.
First clamp the front side of the cart, near the bottom. Because the front is beveled, it doesn't give you a lot of area to clamp on, but you have to make sure your not clamping to the backside of the case as well. Clamp it enough to flex the front side of the case a bit. This gives you an opening in the seam and also relieves the stress on the clips a bit. See pinch.jpg for picture.
Next slide your screwdriver in between the joint as shown in wedge.jpg. Pull the screwdriver in the direction shown until the side pops open. Sometimes both side will pop at once, if not just do the same thing on the other side. Now you should have something looking like open.jpg
Remove the clamp. There are also 2 more clips on the top. As you hinge the cart open, pull the front of cart towards you and the back of it away from you and it should open right up.
This works for most, but not all, types of Famicom carts.
Here are some exceptions:
Namcot carts are really the only ones that are a pain and prone to damage.
The smaller Namcot carts have the clips on the opposite side and there is a thing that snaps together in the middle of the cart. Sometimes that comes right apart, but sometimes it seems almost as if it's fused together. In those cases you really have to muscle it open and often that center pin will break (doesn't really cause any problems though).
The larger blue Namcot carts open like most FC carts, but the front half of the cart is rounded and kinda hard to clamp onto. In addition to that, the plastic seems to be rather brittle in these carts and the tabs often do break off.
A couple of the older Taito games have screws underneath the front label
Oddly I've only run into 2 or 3 of these types and they aren't in any particular order with the game #.
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Hope this will be useful to anybody looking for that info. I didn't find an appropriate clamp yet so for now I just break the pins most of the time.