How safe is building a computer yourself?

I'm interested in getting a new desktop computer soon, and I'm wondering whether I should build it or buy it. I'm very good with software, but I don't have much experience with hardware (recently, I successfully tore apart my Toshiba laptop to replace the fan and add new thermal grease, so I at least do have some experience).

I'm worried that if I build it myself, I'll spend ~$600 on parts and get a non-working computer. I'd rather not waste that much money if it is somewhat likely that it may not work. How safe is it to build it myself?

As long as you take proper ESD precautions and research your parts compatability properly it's safer than it's ever been.

Motherboard choice will be dependent on CPU choice.

RAM is easy - DDR3 is pretty much the only standard in use ATM (mid 2012), DDR2 is considered legacy and DDR4 isn't ready yet - higher numbers are compatible with lower requirements. High end systems (Sandy Bridge-E at this point in time) use a Quad Channel RAM configuration which means you need multiples of 4 sticks of Matched RAM. Mid to High end (most of what an enthusiast would WANT to build) uses DUAL Channel, i.e. multiples of 2 sticks of matched RAM. And low end setups still use single channel, so you you can mix and match brands and capacities across the board.

Pretty much all Graphics cards are PCI express now however just make sure you have adequate PSU power. Here spending more really does make a difference. A name brand 400W such as Corsair is miles better than a no-name brand "800W" (hint the 800W isn't).

Beyond that just be patient, research component compatibility (if in doubt ask) and you should be fine.

How much spare time do you have, and how much is it worth to you?

Building a computer can be a lot of fun, but it's expensive in terms of time compared with the money you can save by finding the exact parts you want at the best price.

I used to build my own stuff quite a bit, but now being married with kids I'll take "hassle free" any day of the week.

I like the suggestions in other answers.
Have one small idea to add.

Look for friends who have built one for themselves.
Friendly experienced people would be a great advantage to have around.
And, if they have built their machines, they would probably like discuss details too.