OK, as someone who has extensively researched caffeine and sports performance as a graduate student, I feel the need to weigh in...
1 cup of coffee isn't going to do much of anything for performance. Seriously. It might make you feel better, though, and this is increasingly becoming one of the preferred explanation for caffeine's performance-enhancing abilities. Most home-brewed coffees will have 60-130 or so milligrams of caffeine. The two field tested running studies used anhydrous caffeine in doses of 3 milligrams/kilogram body weight (i.e. 130 pound runner=59.1 kgs x3= ~180 mg of caffeine) and 5 milligrams/kilogram body weight (~295 mg). Both of these studies found small, but significant, improvements of 1.0-1.2% (O'Rourke et al. 2008, 5-km track running, 11 second improvement for "well-trained" runners; Bridge & Jones 2006, 8-km track running, 24 second improvement) compared to a sugar placebo.
Personally, as an athlete and a coach, I see nothing morally or ethically wrong with using caffeine or similar substances (i.e. sodium bicarbonate) to improve performance. Caffeine is so widely used it's damn near impossible to regulate, which was one of the reasons WADA took it off the prohibited substance list in 2004. Another reason is that even high doses of caffeine (> 6 mg/kg BW) would still yield caffeine levels below the old IOC limit and could improve performance. In fact, one of the seminal papers on caffeine done by Graham and Spriet in 1991 found that only 1 subject out of 9 exceeded the old IOC limit of 12 micrograms/mL of urine.
It's not like caffeine is being abused, either. Recent data out of the doping lab in Barcelona found that caffeine use among athletes (based on urine samples collected and tested between 2004-2008) has not really increased since caffeine was removed from the prohibited list. I don't have the paper in front of me right now, but the facts appear to indicate that things haven't really changed (I believe the author is Del Coso 2011.
In addition to all this, as others have stated, there's shitloads of anecdotal evidence re. caffeine use out there...de-fizzed Cokes by top marathons in the '70s and '80s, black tea that the Kenyans drink a lot of, master's athletes popping No-Doz tablets before tossing the discus. Debsrow & Leveritt (2007) found something like 75% of athletes at the 2005 Ironman World Champs believed caffeine could improve performance, and 89% planned on using some source of caffeine during competition...
If anybody is interested in getting a copy of one of the papers I mention or is looking for more info, send me an e-mail.