Why does Frank peel off the labels from bottles and things?

Personally I saw this behavior as a clever way for the filmmakers to convey Frank's state of mind.

In a film that is all about peeling off labels/layers to reveal the truth beneath the con artist's veneer, the use of this habitual obsession serves to provide a metaphor for the overall theme of the film.

(Note: this is purely speculative and not backed up by any evidence)

I saw this rather differently. Frank is portrayed as someone who's always on the lookout for his next scheme. To my mind he was absent-mindedly removing the labels from branded products because he's half-considering changing to passing cheques from coca-cola, settlers, etc.

Obviously there's more than a certain suggestion of obsessive-compulsive behaviour and the out-of-universe connection between the ways in which corporate entities create their own identities through advertising and Frank's lack of identity (especially when you consider that his wallet, where you'd normally expect to find a man's personal documents, is full of these labels) seems to convey why Spielberg may chosen to add this to the film.

Personally I think it's because Frank has a psychological need to have different identities distilled from his father. He steals the labels unconciously to fulfil a new identity (notice he never takes two of the same label). He keeps them in his wallet as a symbol of his various identities that he has, without one of his own, hence why he leaves his wallet with Carl because he is the first one to see his real identity. Also the fact that he only rips the main label and always puts it in his wallet (almost like a killers MO) is symbolic of the fact that he keeps his name Frank throughout but changes his surname. This is my theory anyway.

Let's not also forget that really, Frank is just a kid. And kids collect things. I can remember when I was probably 10 or 11, while my mom was clothes shopping, I would sometimes keep myself occupied by running around and collecting labels from clothes. So there's also the distinct possibility that Frank is doing something similar.

However, I think a better answer is that Frank owns nothing. He has no credit cards, no photos, nothing that ordinary people would put in their wallets. However, he still has a need to be normal, to feel normal, to have something of his own and to be taken seriously. So he fills up his wallet with labels, just so that there's something in his wallet. Let's not forget, when he tossed his wallet at Hanks' character, he didn't even bother to look inside at first. Most likely because it had substance to it. Had it been empty and light, it probably would have raised suspicion immediately, like, "Why are you tossing me an empty wallet?" So, I think this theory probably (pardon the pun) holds more weight than my other one. To borrow a line from this analysis of the film:

And, well, what is really in all our wallets, after all, but a series of labels? Each piece of I.D., each bank card, each membership card, is a label, a "brand" as it were, identifying the bearer as this or that kind of person.

I think these psychological analyses are just overthinking things here. The wallet stuffing is merely part of the con - Frank is trying to pass himself off as someone else, someone real - and real guys tend to have full wallets. It adds versimilitude. He chooses labels because (a) they are conveniently at hand; (b) their variation in image produces a convincing imitation of a bunch of legitimate documents in a wallet, seen only on edge; (c) Labels torn off of containers are likely to 'pass under the radar' - lots of people like to tear off labels once in a while [I myself sometimes like to rip the labels off of my peanut butter jars].