I've been bitten by a lot of things!
My rating is based on pain and amount of blood/superficial damage
10 being the most ouchy
Budgies 9/10 - they always get you between the fingers or in some delicate place and they slice and cling and don't let go. The worst part is they are so delicate that you try not to hurt them as you pry them off your bleeding flesh... and the second you remove them they have sunk their razor sharp beaks into a new part of your flesh :/ I am more fearful of a budgie bite than a cockatoo bite. On top of less pain, cockatoos are also easier to remove.
Cockatiels 8/10 - nippy little things, but slice less often than budgies. They bite more often though, cockatiels are such temperamental little things.
Lovebirds 7/10 - they "bite" more often but squeeze rather than slice and so while you end up bruised there is less often blood.
Green Cheeks 7/10 - up until recently I would have put them lower than this (probably at a 4/10) but my new girl, Colada, changed my mind. When she bites she is as bad as a budgie, she hangs on and slices!! I have regular war wounds from loving my little skittle turkey. I have birdy love bites all over my neck and hands!
Galah 3/10 - Even when Larry meant to bite hard he wasn't even as bad as a lovebird... galah beaks are almost soft but there is still a bit of power behind it. He never broke my skin but did bruise me pretty badly once. I have picked up many wild galahs and once again, even their bite was pretty weak.
Sulfur Crested 7/10 - These guys have always seemed kinda unpredictable and when they want to hurt they can. I was bitten as a child so its not a very fair comparison, it probably hurt more then than it would now
Nanday Conure 9/10 - OUCH! Power and slicing coupled with a cheeky challenging attitude and I came away with a few bloody fingers
Rainbow / Red collared lorikeet 6/10 - these guys are very beaky but give you fair warning when they arent in the mood for play. They have a beak shape that stabs rather than slicing or squeezing.
Birds I have owned/handreared/bird sat who have not bitten me even once...
Sun conure
Eclectus female
Alexandrine
Non-parrot bird ratings...
Magpie1/10 - these guys have nothing on a parrot LOL
Noisey Miner 1/10 - again, squishy little beaks
Currawong 2/10 - a more powerful beak but still no parrot
Kookaburra 3/10 - we had one who frequently visited for feeds... and while they dont mean to hurt, they can have terrible aim and get you in the process of taking food from you. This is a much more powerful beak and bit hurt a little bit.
Goose 3/10 - LOL!
Other critters...
Eastern Bearded Dragon... 9/10 OUCH! :/
Carpet Python 3/10 - little needle teeth do nothing
Central bearded dragon 6/10 - so much less painful than the big fierce eastern!
Water dragon 7/10
Rat 6/10
Mouse 4/10
Dog 6/10
Cat 8/10 - infections are not nice
Monitor lizard... I haven't been bitten by one but I give them a 10/10 rating and never want to experience it