Chesstempo has tagging - and honestly, once you're past the low-level (<1400) level problems, they're nearly useless, as once they're harder than that point, there are so many tags that it's more confusing to even have a clue of what the tags for the problem are than just learning the pattern on the board.
The danger with tagging as well is that it makes people who learn what a 'pin' is, over-rely on it. When rookies start seeing a potential pin, they get super excited, and almost always want to play it. What they don't see is the combo 3-moves down the road that refutes the pin. (The Bh7+ greek-gift type line is a common example of a pin refutation.) In those cases, those players may have been able to see the ensuing combo if they'd just ignored the tag and calculated out the position more deeply, but their brain clings onto that 'tag' they recognized, and it blinded them to the ensuing combo.
I'm doing a lot of chesstempo now, and you wouldn't believe the number of 'tag refutation' problems there that have a higher (1700+) tactics rating and are based almost entirely around refuting a seemingly obvious and inviting 'tag' position. They're however, usually very straightforward to solve (seemingly well under 1700 level) once you tell yourself to ignore the 'obvious' tag, and calculate it out as a de novo position so you're not distracted by the tag.
Tagging positions can help organize patterns in your brain though. Probably not required, but might help some people.