Q:

What model circuit breaker is this?

I live in an old 50 + year old house and it still has the original circuit breakers. I am trying to search for one that died, but don't know the model or even if they make these anymore. If any electricians out there can help me out, I would greatly appreciate it.
I haven't removed it (Kinda' scared to do so and get shocked), but here's a pic.

Here's more pics on the Fuse Box.

A:

While I think you'll be smart to hire an electrician and consider replacing the whole panel...
Circuit breaker boxes vary in style.  You have to buy the correct replacement breaker for your specific box.  To determine what you need, examine the box itself.  Somewhere on the box will be the name of the manufacturer.  
Tip:  "Square D" is not it.  (Personal experience talking) - Square D MAKES breakers to fit numerous types of boxes.
If you can't immediately find the name of your panel maker, go to this link:
Online site for buying circuit breakers
They list a lot of manufacturers there - see if you can find yours.  
Now again - because you yourself said you're scared to remove it - PLEASE DON'T.  This is potentially deadly work you're considering and if you don't know what you're doing, this is NOT a project you should learn using the trial and error method!!!
Update - after looking at the extra pics - your breaker box is by "American".  First manuf. on the list.  The labels on some of your breakers indicate it.

A:

The answer is actually staring you in the face under all that paint: Electri-Center. These are, in theory, Seimens breakers. (I say in theory because the box looks like someone's taken a hacksaw to it, which means they may have replaced the guts with some other brand of hardware.) They should be available at Home Depot. Shut off the mains, remove the bad breaker, take it in to Home Depot and make sure that you match them. Alternately, take it to an electrical distributor and they'll be able to match it. 
However, I would STRONGLY urge you to hire an electrician and have them evaluate the condition of the panel because of a few of the things that I see inside the box. First of all, there are wire 'colors' that mean specific things. What I'm seeing is a red wire and a green wire going into the hot side of some of these breakers. Red is 'meh' but not 'right'; it should only be used for the switch leg of a circuit but it's OK for it to be 'hot'. Green generally means ground and anyone working on the far end of that cable is going to get a surprise unless they're using a non-contact voltage sensor. There are distinct signs of hackery and/or overloading and/or age-induced overloading on this panel, and with that plus the aluminum wiring and the age of these breakers, I would be extremely leery of just replacing the breaker and assuming that it will be fine. 

A:

TL;DR: If you haven't incinerated yet, replace that panel as soon as possible, if not sooner!!!
It looks like your panel may have been an archaic piece of equipment (fuse box?!) at some point which someone (illegally!) gutted and replaced with the guts of a FPE Stab-Lok panel.  Sadly, what they did is replace old, but somewhat-functional service equipment with total garbage that is liable to not do its job whatsoever when called upon.  Yes -- these breakers, especially the two-pole types, are known to consistently fail to meet trip curves, and the two-pole versions are susceptible to an internal mechanical jam that turns them into fancy jumper leads.
P.S. the labels on the breakers are a dead giveaway -- one of them states "Stab-Lok" on it in somewhat messed up letters, and both of them have visible Type NA markings on them; unlike say a BR breaker (which fits several different makes of panels), the type NA is only compatible with FPE Stab-Lok panels.

