HP Fans: On wands and magic... What sort of magic could be performed without wands?

Remember on PS, Dumbledore clapped his hands and the decorations changed, Quirrel snapped his fingers and ropes suddenly sprang up and wrapped Harry? It just nagged me that Dumbledore could have performed some magic even if he was disarmed (nevermind his pact with Snape and all that), and this sort of wandless... show more Remember on PS, Dumbledore clapped his hands and the decorations changed, Quirrel snapped his fingers and ropes suddenly sprang up and wrapped Harry? It just nagged me that Dumbledore could have performed some magic even if he was disarmed (nevermind his pact with Snape and all that), and this sort of wandless magic was mentioned at least twice in the series but wasn't expounded. So what magic could be performed wandless? Is it just simple ones like changing the House banners, yet, Quirrel's act wasn't that simple at all. Sorry for the not-so-straightforward question, I find difficulty simplifying this. :)
Update: Yes, but Apparition, Occlumency & Legilimency requires more of concentration and being an Animagus requires practice and concentration, too. I liken them to Potions Making, where there is little magic involved, just the correct ingredients, method and patience. @Navigator, Summoning Charm and Lumos requires a wand. show more Yes, but Apparition, Occlumency & Legilimency requires more of concentration and being an Animagus requires practice and concentration, too. I liken them to Potions Making, where there is little magic involved, just the correct ingredients, method and patience. @Navigator, Summoning Charm and Lumos requires a wand.
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