Which processor do you Have or do you plan to get? That's important.
As hunter315 already mentioned, you can get an Intel Core i3/i5 CPU that has integrated graphics abilities and use it with an H55 motherboard. This is NOT meant to play games with by ANY stretch of the imagination, but will give you a perfectly suitable desktop PC without a discrete graphics card.
I built a Core i / H55 system for my in-laws not too long ago. Works great.