Yes, you can.
ATX - The largest with more than 2 PCIx16 slots or more than 5 PCI slots. Micro ATX - Medium sized board with upto 2 PCIx16 slots and 3 PCI slots. ITX - Mini board with very few expansion capability. Only meant for machines that are to be used as Internet browsing thin clients.
I put in a ATI HD 4650 PCIx16 $69.99 in mine and it runs GREAT! Just plug it in to slot>turn on computer>install the drivers>reboot the computer and you are good to go.
CPU > Motherboard > RAM > I/O (Graphics, Sound, Hard drive Controller, etc. ) Generally, one chooses a CPU, then based on the CPU requirements, amotherboard then RAM and so on. However if you are looking to use a specific graphics card, you would need to find the requirements for that model. The interface needs to match or be compatible, such as PCI express. If your video card uses a PCIx16 2.0 slot, your motherboard would need to be able to support a PCIx16 2.0 card. But if your board had a PCIx16 2.1 slot, it would still work because the 2.1 revision is backwards compatible. However, cards such as a PCIx1 slot is not compatible with a PCIx16 card. There are also motherboards that support SLI orCrossfire X This is a special link that allows to or more video card to work together. Some motherboards support SLI some supportCrossfire X some support both. AMD/ATI usesCrossfire Xto link their video cards, nVidia uses SLI. These are not cross compatible, i.e. SLI between an AMD card and nVidia card. All in all, graphics cards do not require a specific motherboard, nor do motherboards require specific video cards. Also, if the motherboard has the option for SLI, and only one graphics card is used, an AMD card will usually work just fine (Crossfire Xrequires 2 or more cards) and vice versa. One more exception is the new AMD APUs. These are processors with a GPU [Graphics Processing Unit] built in (notexactly but for simplicity we'll call it a GPU). These do have requirements for specific graphics cards if the added APUbenefitis to be utilized. Not required to function, just to utilize thebenefits.To sum it up, most of the time there are no specificdependenciesother that it fits in the slot provided (AGP had different voltage tabs that required them to match however PCI = PCI, PCIx1 will fit in a PCIx[1,2,4,6,8,16] slot. One more thing to consider, nowadays they have boards with PCIx8 - mechanically x16. this means the physical slot is a x16 slot, but it acts like an 8x slot (it only has the data throughput of an x8 slot) so a x16 would fit and work butwouldn'tgo as fast. You generally see this on moterboards with multi PCIx slots. So a board might has 4 PCIx slots, (x16, x8, x4, x4) so the first slot logically would have a 16x data bus, the second logical slot would have a 8x data bus, and the last 2 would run at x4. I hope this doesn't overwhelm you, its is a bit much for such a simple question. :) anyway hope it helps!