In Illinois, the procedures for Requests for Admissions are found in Illinois Rule 216. An important companion is Rule 219(b), which gives you options if your opponent arbitrarily denies your requests, thereby forcing you to spend money to prove facts at trial. Rule 219(b) reads as follows--
Expenses on Refusal to Admit. If a party, after being served with a request to admit the genuineness of any documents or the truth of any matters of fact, serves a sworn denial thereof, and if the party requesting the admissions thereafter proves the genuineness of the document or the truth of the matter of fact, the requesting party may apply to the court for an order requiring the other party to pay the requesting party the reasonable expenses incurred in making the proof, including reasonable attorney's fees. Unless the court finds that there were good reasons for the denial or that the admissions sought were of no substantial importance, the order shall be made.
If you seek costs based on Rule 219(b), your opponent has some options too. As the rule states, he can argue that there was a good reason for the denial or that the admissions sought were of "no substantial importance."
What's a good reason for denial? Though you won't find too much case law on the topic, a good reason exists when admitting the requests would require your opponent to concede his entire case. Here's how one court made this point--
[Rule 219(b)] requires that the matters asserted be proved and that the opposing party lacked good reasons to deny the request. The policy behind the rule is to promote settlement and simplify litigation. Here, plaintiff filed a "Request to Admit," which requested that defendants admit, among other things, that the fire began in the larger building and spread to the smaller one and that plaintiff sustained $ 216,761 in damages. Plaintiff, in essence, wanted defendants to concede plaintiff's entire case. Clearly, this is not the intent of the rule.
In Exchange National Bank v. DeGraff (1982), 110 Ill. App. 3d 145, 441 N.E.2d 1197, we held that defendant bank had a good reason to refuse to admit the allegations sought by plaintiff because the bank's admission of the plaintiff's requests would be conceding away its whole case. We went on to state that "[i]f the rule is extended to all controverted matters which become 'proven facts' only through a general verdict or judgment, the prevailing party to an action would presumably be allowed to recover fees and expenses routinely. We do not believe this is the intent of Supreme Court Rule 219(b)." Similarly, in this case, defendants were not required to admit liability.
Chem-Pac, Inc. v. Simborg, 145 Ill. App. 3d 520, 526 (Ill. Ct. App. 1986) (some citations omitted).
Keep in mind that in order to obtain costs under Rule 219(b), you don't have to win the underlying case, but merely prove a fact that was previously denied. See, e.g., "The Harsh Reality of Supreme Court Rule 216," by Richard Kessler (pdf). Finally, if you decide to seek costs for your opponent's denials, you'll have to ask the court to make a specific finding as to why there were no good reasons for the denials and why the requests were of substantial importance. An order that merely recites the general language of the rule may not withstand appeal. See In re Estate of Smith, 201 Ill. App. 3d 1005 (Ill. Ct. App. 1990).