In Following, Cobb gives a Lloyds bank credit card to Bill in a coffee shop. Why did Bill accept it?
Why wouldn't he accept it? He got a credit card as a gift to use for his own needs and he's already done other illegal stuff at that point and he wasn't really considering the moral or personal consequences of those things at all, let alone the possibility that Cobb had something more sinister in mind for him.
Let's look at Bill's situation. He is basically unemployed, claiming to be a writer but in fact only wishing/pretending to be one. He repeatedly said that he can't afford this meal (and likely other things in Cobb's lifestyle). So first of all, he could definitely use some money. And at that point Bill was already pretty emerged into and fascinated by Cobb's illegal activities and taking a forged credit card from him wasn't really beyond anything he already did together with him. Besides that he started to look up to Cobb and also to enjoy this lifestyle, as also evident from the particular dialogue of this scene
Cobb: You're developing a taste for it. The violating, the voyeurism, it's definitely you...I think before long you'll have developed a taste for the things that go with the proceeds.
Bill: Such as?
Cobb: Well, all this.
Bill: Do you make all your money through burglary?
Cobb: No, not all of it. In fact, you're gonna pay for this.
Bill: I told you, I can't afford to pay for this.
Cobb: It won't really be you. It'll be D. Lloyd that pays for this. I thought I'd give you the pleasure of pretending to pay.
Bill: What am I supposed to do with this?
Cobb: Sign it, in your own handwriting. Then you can do anything you want with it.
To which Bill eagerly and smilingly signs it. It was just the next step in pretending to be someone else and enjoying the advantages of that. And Cobb realized this, in fact he chose Bill exactly because he saw that this was a completely orientationless guy looking into other peoples' lives that was easy to manipulate into Cobb's own ways (also remember how he manipulated him into changing his appearance, much to Cobb's own likeness).