This varies a lot so it's hard to write a definitive answer. But if you're bouldering (full stop) and you think you're going to fall off (high in your grade) and your concerned about your landing, you want a spotter.
Height is pretty much irrelevant.
The spotters jobs include:
- Making sure you don't land on your head
- Ensuring you land on your feet
- Ensuring you land on the mats
- Moving the mats around so that they're under you
- shouting encouragement...
- Telling you they did it last week and it's easy, you're just doing it
This is just as relevant at 1m as it is at 6m.
Remember a spotters job is not to catch you. They are there to ensure you land safely on the mats. This may mean they push you as you fall or flip you onto your feet but they should never try and actually catch you; this will likely just result in both the climber and spotter getting hurt.
This doesn't mean you always need a spotter; they just add an extra dimension of safety. It's up to you to decide if you feel you want one or not. It's likely advisable if the landing is bad (not flat and/or covered in rocks, etc) or you're really pushing your grade and may have an uncontrolled fall.
We seem to be getting into the realms of when does bouldering stop being bouldering and start free soloing. TBH I don't know, I don't think anyone does. It really depends on your own confidence. Personally I don't think I've climbed over 3m or so without a rope. If you're brave enough to climb higher than this with just mats then good luck. A spotter may help.
Here's some advice form Climbing.com on spotting on high ball problems (emphasis my own):
Never assume you’re being spotted and don’t be afraid to request one.
As climbers, we’re responsible for our own safety. Spotting a
super-highball can be dangerous, and the main goal for a spotter is to
guide the falling climber onto the pads, not to catch her or slow her
fall. Discuss the landing zone, how you might fall, and where the
spotters should stand. As the climber falls, the spotter should aim to
grasp her hips and fall with her toward the pads. With really big
highballs, use a “floating pad” to cushion the impact: Two people hold
a regular pad a few feet above the main pad layout, tracking
underneath the climber and letting go when the climber hits this pad.
The climber will hit the floating pad first, slowing her fall, before
landing on the layered pads below.
While spotting, keep fingers and thumbs together in a cupped position
(spoons) as opposed to spread out (forks). This prevents finger and
hand injury. With arms up, keep your elbows and knees slightly bent.
It's very subjective and you really need to make you own decision here but a spotter will help move the mats into the correct position if nothing else.