Most of the video cards today or even older ones have dual video outputs. The older ones tend to have 1 DVI and 1 VGA. The newer ones usually have 2 DVIs and most often include an adapter for DVI -> VGA. There is one that goes the other way (VGA -> DVI) but in reality it wont up convert the signal, it'll stay analog.
To make it more complicated, DVIs come in single link and dual link. Dual link has more bandwidth and if you look at the connecter, there a few pins with a +. The single link only has a few pins with a -. Most of the video cards have the + and monitors have the -. What to do? Just get the single link cable and itll be fine. ONLY GET DUAL LINK if BOTH monitor and video card support it. Look for the + pins.
With that out of the way; NO not all monitors come with DVI. Ask or look. The DVI connections are a lot bigger, roughly twice that of VGA. And if it is DVI, itll most likely have VGA.
You can get two monitors running, one with DVI and one with VGA or two DVIs or two VGAs. Preferrably two DVIs because of consistency and better image quality, especially in LCDs.
You can also get two separate video cards. Depending on which you have, you can get a mixture. Older boards usually have AGP and PCI. So you can getone of each. Newer ones will have either 2 PCI-e and PCI or 1 PCI-e and PCI.
Now if you were getting two new monitors and want it nice, I suggest getting a card with dual DVI and 2 exact monitors with DVI.