There are a few different kinds of issues that come up.
Software updates are a pain. Most of the time they work fine (especially now that Apple has more commodity hardware and public OS betas). Sometimes there are issues though and it is just always smart to wait a few months while they are figured out. If you are the sort that always wants to be running the latest OS version you'll find this frustrating or you'll spend a lot of time updating. My MacBook Pro was running Yosemite from day one. My hackintosh is still on 10.9.5. There are a few other minor software issues that come up.. iMessage is always a chore to get working.
On the hardware end you get much greater build to order flexibility. You are limited in hardware to largely things that Apple uses somewhere in their product line but this still gives you quite a few options since there are a few very useful combos that Apple just doesn't sell. My configuration is basically an iMac without a screen and with the Mac Pro graphics card. A Mac Pro would require me to buy ~$2000 of Xeon hardware and a second GPU, neither of which I need. An iMac would saddle me with a mobile GPU and non-replacable glossy screen. As a bonus I have 5 different internal SATA drives (with room for more) and a Blu-Ray burner.
That said, there are a lot of things about Apple hardware that I miss. I don't have any Thunderbolt ports though and the graphics card is full of legacy DVI ports instead of useful DisplayPort ones. The machine is large and uses way more power and throws off way more heat than an Apple machine. I had to do some careful design work to get something quiet and it is still not as quiet as Apple hardware. Sleep has never worked reliably. Boot screen support for my graphics card doesn't exist so I have to physically unplug video cables if I want to see what is happening during boot up (say if I want to reboot in Linux or Windows or from a recovery partition). The audio ports don't have the third contact for a headset like Apple's do so I need a USB headset.
Overall, as a desktop solution for home use, non-commercial software development, and gaming it lets you be more cost efficient with your computing hardware at the price of time spent researching and tinkering. Particularly so if your use case is one that Apple doesn't cater to like gaming or anything that thinness isn't a top priority. Once it was set up I don't tend to have problems. My hardware was ordered with Hackintosh compatibility in mind though. Problems typically tend to be clustered around OS upgrades or hardware changes rather than day to day issues (except for issues due to hardware constraints like sleep/wake and boot screens). It is otherwise pretty stable.
I'd never recommend it for a laptop, a non-technical person, anyone who has more money than time, or anyone who needs something reliable/with manufacturer support/help. I wish I could justify a Mac Pro for my use case but I can't at 3-4x the price. I have a MacBook Pro for serious work which lets me take on more risk of having the desktop out of commission due to any issues.