It's not very dangerous as such. Get an anti-static strap and work grounded and you should have no real reason to break anything. There is little if any money to be saved by doing this, however. The benefits come from being able to hand-pick components that might be more up-market than a mass market vendor would use by choice.
The last system I properly built from scratch as my main PC was quite expensive - it had SCSI disks and a fairly upmarket motherboard. More recently (when I moved to the UK in 2004) I recycled some components into a pair of small-footprint machines with micro-ATX motherboards. I put some effort into these to keep the interior tidy - cable ties and sticky-backed plastic hooks, quiet molex fans and some other niceties. They did me quite nicely for about 18 months after I got here.
Since then I have just bought secondhand PCs - mainly two socket Xeon or Opteron workstations used for data warehouse development (new ones are expensive but secondhand ones are much cheaper). While I didn't assemble these from scratch I did do memory and CPU upgrades (single-dual core CPUs and suchlike) and fitted third party RAID controllers and arrays of SCSI disks.
Given how cheap a secondhand PC is (you can get ex-lease machines for less than £100 off ebay) there's no real point in building a system unless you have some specific requirements. It can be worth doing for the experience if you haven't done it before but don't expect to save much if any money doing it.