If I borrow money or charge something on a credit card, and then do not pay for it, can the other side pursue me if I have not given some kind of collateral?

Generally, a creditor who does have rights in collateral has a more secure position than a creditor who does not, but the mere fact that a creditor has no collateral does not mean that it cannot pursue a debtor for money loaned or charged.  I have had several people ask me questions about this during my practice, and I have been surprised by the level of misunderstanding I have encountered on this subject.  If in doubt, debtors should consult counsel concerning their rights and obligations on such things.