Problem with superglue...

...is it tends to cause 'frosting' (white residue) anywhere its curing fumes reach. You can remove this easily enough for glass and ceramics, but not so much for plasics and polymer paints, which may not be so good for toys and ornaments where the look of the item is part of its value/function. I have experimented with using masking tape to protect the area around the joins when fixing plastic objects, it works somewhat, depending on the complexity of the item's shape.

The join created by SG, of course, is very strong, though brittle, which is good if the material you are joining is rigid, not so much if it has some plasticity.

@Richard12: very interesting - I knew cyanoacrylate was often used in brain surgery but didn't realise it was invented explicitly for that sort of thing!

For acrylics you can't go past one of the Acrylic Joiners (I use Acryfix and WeldOn brands*). Since this doesn't so much glue the stuff as chemically-weld it. If done right (which takes more equipment than I have access to) you end up with the origional unbroken piece. Even done at work-shop level you get close.

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*false-nail remover can work too, depending on the type - the stuff used to be exactly the same as the industrial version, but it is mildly toxic on skin-contact so it has mostly been replaced with other chemicals that don't do such a good join, but don't poision people getting frequent manicures either