Hello, I recently purchased a new GTX 1060 FTW+ on Amazon.  Card is brand new in original package, tightly sealed.
When I opened the box I noticed that it has no driver install disc with it, or any connector for my monitor to hook into. My monitor is very old, like 10 years, but I have always been able to connect to my older cards, a 450 and a 560TI. The older card came with a exterior connector, but they seem slightly different and won't fit on the back of the new 1060. Old connector had 4 small pins around flat connector, new card has the flat slot, but not the other 4 pins, so it wont plug in.
 
Do these cards not come with driver discs or connectors, ( I saw a unboxing video and that guys card had a driver disc at least) or are they simply missing from my package?
 
Thanks.

The disk usually stuck inside the manual and would fall right out.  Did you get the manual?  Did you get the power adapter or poster?
 
When it comes to drivers, what is on the disk is just a functional starting place.  Your best off using the latest drivers available at http://www.evga.com/support/download/
 
As for the DVI to VGA adapter you are referring to, this graphics card and most of the 10 series graphics cards do not support them.  The DVI connection needed for adaption is DVI-I, but these cards are DVI-D.  If you need to adapt to VGA, your best bet is to look into a passive Display Port to VGA adapter.

This is the only Cable that Comes with your Card:

 
 Did you get your EVGA Case Badge?
                                                   EVGA Case Badge

Other than the card, all that was in the box was the 8-pin cable, the user guide, the white guide about requirements, the little badge, and a poster. I did not get the 2 stickers shown above, or the driver disc. Believe me, I looked all over to make sure I didn't simply misplace it during opening.

I am planning on getting a newer monitor soon, but was trying to wait for some holiday sales.  Should I go with a HDMI monitor, or try to get a VGA adaptor and make sure the card works?

DO NOT BYPASS THIS "but not the other 4 pins, so it wont plug in."
Do Not Make Shift a Analog To Digital Connector. Use on a DVI-I Port Only.
You only have a DVI-D Port and you CANNOT USE the Analog To Digital Connector on your Card.
DVI-D, DisplayPort, DisplayPort, DisplayPort, HDMI  Time for a New Monitor.
 

 
A DVI-D connector on a graphics card sends out a digital signal only, while a DVI-I connector, which carries both an analog and digital signal, can send out a digital signal (for digital displays such as flat panel LCD monitors) as well as analog signal (for older displays such as a CRT monitor) using a DVI to VGA adaptor shown below.  The graphics card shown in Figure 1 which shows a DVI-I connector contains more pins than the DVI-D connector shown in Figure 2.  The extra pins on a DVI-I connector carry the analog signal which the DVI-D connector does not have. 

Ok, so I purchased a new ASUS VG248 monitor so I should be good to go. However, I went to install the card and realized that it takes 8 pin connector, but my power supply, being older (its an OCZ GXS700), has only has 6 pin connectors. The card came with the adaptor posted above, but I've heard that using them can cause instability with the graphics cards. 

Is it safe to use the adaptor, and do you just plug one 6 pin into it or two?

I've already spent more money then I really wanted to, and don't really want to buy a new power supply if it can be avoided. The one I have still runs just fine.    I picked out the card using pcpartspicker.com, and it didn't flag any incompatibilities with my current build, so I thought I was safe.

Using the included adapter with two 6 pin PCIE power plugs to the single 8 pin PCIE power plug will work fine. Plug two 6 pin plugs in, not just the one.
 
It's the Molex to PCIE power adapters that have been known to mess things up badly on occasion.

Great!  Thank you!

Well, now I'm not sure what to do.  First I had a issue plugging the 6-pins into the adaptor, I think one of the pins was bent. I managed to straight it enough to get the second 6 pin in, but now I can't get the 8-pin end to plug into the card. I pushed as hard as I dare, but it still wont go in. The metal sockets don't seem perfectly straight, but it doesn't really feel like they are the part resisting. I've tried evening them out with a paper clip, but it doesn't work

Terrek
Well, now I'm not sure what to do.  First I had a issue plugging the 6-pins into the adaptor, I think one of the pins was bent. I managed to straight it enough to get the second 6 pin in, but now I can't get the 8-pin end to plug into the card. I pushed as hard as I dare, but it still wont go in. The metal sockets don't seem perfectly straight, but it doesn't really feel like they are the part resisting. I've tried evening them out with a paper clip, but it doesn't work

Time to call in someone else to assist you. Any further tinkering could cause further damage.