Several years ago, a BCG Attorney Search article detailed the dangers of trying to use offers from other firms as leverage at your current firm, commenting on the fact that such offers are often wolves in sheep's clothing.
This article addressed most firms' usual motivation for extending a counteroffer; a candidate's common motivation for accepting it (i.e., the "natural inclination . . . to stay with the devil you know rather than to dance with a new one"); and what a candidate's future will probably hold at that same firm if they do choose to stay.
What the above-referenced article did not address, however, is how to avoid walking down the counteroffer path in the first place. It also did not address the secondary consideration attendant to any counteroffer scenario. You have put yourself on the market with another firm or firms (ones that are very often competitors to your current firm); taken the time to meet with them and exchange professional goals and desires; and asked them to invest their time in meeting with you (often over the course of several weeks or months). Once you obtain an offer, you use it merely for leverage, and responding to the new firm, "Never mind; I think I will stay where I am."
Ill will is never created where this exchange of meetings and interviews is an honest and legitimate exploration of the marketplace. People turn down offers from new firms every day because, for example, the work doesn't suit their growth goals, chances for advancement are murky, relocation is problematic, they didn't feel a "click" with the group, and other reasons. Firms understand this and accept such reasons for decline as acceptable and par for the course in the marketplace.
In contrast, ill will is created where sincerity is absent. Simply put, what firms don't understand is your reaching out to them deliberately in pursuit of an offer but, it seems, only desiring to use that offer as leverage to obtain a better deal (or counteroffer) at your current firm. This type of scenario is a very dangerous game of "one upsmanship" or "better dealing," which firms do not forget.