Cheating isn't new in baseball; to an extent, it's an art form. Traditional approaches include stealing signs, 'peeking' (hitters trying to check the catcher's position), and baserunners trying to get an idea about pitch type and location from the catcher. 'Peeking' tends not to work, as it can generate brushbacks, and catchers may give deceptive initial location, as Jason Varitek does.
Baseballs can be 'doctored' by cooling them (reducing distance) and Whitey Ford/Yogi Berra were known for innovative 'cutting' of baseballs. Who can forget the spitter, Vaseline ball, et cetera from the likes of Gaylord Perry, John Wyatt, and others?
Club approaches to 'cheating' include tailoring the field (Tiger Stadium grass growing to prodigious lengths to slow grounders), manicuring foul lines to help or hurt bunting, fluffing the dirt in front of the plate to slow ground balls, and watering the basepaths to hinder speed. The Twins have been accused of adjusting the air conditioning somehow, but I can't imagine that makes a difference.
Non-traditional cheating includes corked bats, corked players (steroids, human growth hormone), and electronic surveillance (the Cleveland Indians were accused of having a surveillance camera for signs). I'll add more as time and memory permit.