As the question states.
I've been looking around at different motherboards and I have seen on these boards, that this boards do not have any particular connectors for certain graphics cards. Does this mean that a motherboard can take any graphics card regardless of the fitting?
Generally most motherboards have 1 or 2 PCI-E x8 or x16 slots. These will be the ones that the graphics card will go in. Exactly what the card needs will depend on the card, some will use either x8 or x16, some will need an x16 slot, some may even be x8 only (anything is possible).
So while most of the time these days just about any card will fit into just about any motherboard there are always exceptions and you should check the requirements on the card and features of the motherboard.
Higher end graphics cards may also require additional power connections or capacity from the main system power supply.
Update - You indicated you were interested in the
MSI B150M and a Nvidia Geforce 750
That is a family of motherboards and a graphics chip rather than a specific graphics card from a manufacturer. Generally they look to be compatible however you need to check specific parts to be sure rather than product families. You also need to verify you meet the power supply requirements since that graphics chip will need 55 W minimum on top of your CPU, HDD and whatever else is in the box.
The answer depends on a few factors which means its a yes and no kind of answer. Due to how the question is stated, that would make it a no.
But I'll clarify.
There are a few different types of sockets: PCI, AGP and PCI-Express. Although the former two are ancient by now, I still occasionally find an old pc with an AGP slot. Obviously an AGP videocard won't fit in a PCI-Express interface and visa-versa.
That said, PCI-Express has its own standards too: PCI-Express 1x, 2x, 4x, 8x, etc. The higher the number, the faster it can perform. Although graphics cards are backward compatible, a significant speed decrease will be noticable in these cases and as such, you want to avoid that.
In addition, the more powerful graphics cards have additional ATX power connectors, and as such require a capable ATX power supply with sufficient output. The power supply is not part of the mainboard though, but to be thorough, I added the information regardless.
