They have low self esteem. Try to ignore it.
I usually ask why they're so hard on themselves and encourage them to be more boastful. Then I introduce them to the new kid and walk off.
Its best to ignore them, however sometimes it's difficult to ignore because you hear it again and again. In those circumstances its worth pointing out the truth to them by contradicting what they are saying.
1. Say shut the hell up, no body wants to hearr it.
2. Ask them why they are so insecure as to need to brag to or insult other people.
I tune them out. Sometimes I'll just walk away, I can't only take so much of the "Praising Myself" moment.
you guys are sissies. instead of ignoring them, simply troll them.
1 brag more than them
2 for every brag (claim), contest and prove them wrong
3 sarcastically be amazed in WHATEVER THEY SAY. even if they're not bragging
4 brag when they're not bragging
5 when the opportunity arises that you think he/she will brag, brag 1st that he/she can do it. (eg a wild mars appears, immediately tell him/her and his/her friends, did you know that (insert bragger's name here) already bought the moon? he/she's gonna live there someday. simply put don't let him/her speak by putting words into his/her mouth)
tiring but fun if your common friends agree on your opinion about his/her bragging behavior. shutting up bragging bastards can be fun too! :D
Point out the holes in his/her bragging
believe them and tell them your neighbour has also done it or has it
Just ignore them. They'll get tired and bored, and the'll stop. You can go along with them if you think it's fun~