Indeed they have!
First off, for anyone who's unfamilar with the activity, B.A.S.E. jumping is the act of parachuting from a building, antenna, span (i.e., bridge), or earth (i.e., a natural landscape feature), as opposed to leaping from a plane. As far as the first three in particular are concerned, there's often trespassing involved and a rapid getaway required, unless the jump takes place as an organized publicity stunt.
As the tallest building west of the Mississippi, at 1,149 feet the Stratosphere is an obvious target for any B.A.S.E. jumper and we know of at least two successful feats, neither of which took place with the consent of the owners. However, a prior incident took place that was a prearranged stunt, organized -- no surprise here -- by notorious self-promoter Bob Stupak.
This event actually predated the Stratosphere and was in fact arranged to mark the opening of its predecessor, Stupak's Vegas World. He hired a Native American for a fee of $1,000,000 to jump from the roof onto a cushion (whether with or without a parachute remains unclear from accounts we've read, but it seems without) -- and then charged the unsuspecting stuntman a $990,000 landing fee. Pure Stupak!
Fast forward a couple of decades to the first jump we know of from the Stratosphere itself, which took place on Sept. 1, 1999 and involved B.A.S.E. jumpers Eric Lee and Mark Lichtle, who successfully scaled the guard rails and leapt from part of the window-cleaning apparatus. You can see footage of the entire stunt, from their arrival in the Top of the World elevator, to the jump itself, followed by the hotfooted exit once they hit street level. You can view using Quicktime or Windows Media Player at AerialExtreme.com website (scroll down past the other videos), where you can also download both programs for free, if you don't have.
The only other instance that we know of took place in 2007, performed by renowned (or notorious, depending on how you look at it) B.A.S.E. jumpers Iiro Seppänen (of Finland, now retired) and jumping partner Jeb Corliss (U.S.). From this video clip, you can see how the pair smuggled their gear up the tower hidden inside an oversized plush puppy toy and hear the bemused shrieks of observers as they witness two men plunging off the side of the Stratosphere Tower. Other successful jumps this fearless duo's clocked up between them include the Eiffel Tower (from which one of the earliest ever B.A.S.E. jumps took place in 1912, with lethal results), Golden Gate Bridge, Grand Canyon, Seattle's Space Needle, and the Petronas Twin Towers in Malaysia.
While researching this answer, we also came across an account of someone having B.A.S.E. jumped from the roof of the Wynn in early 2007, and there have doubtless been other examples that we don't know about -- it's not an activity that the casinos are keen to encourage or publicize. That's doubtless particularly true of the Stratosphere Tower, which has witnessed a number of suicides over the years (see QoD 10/18/2005), and is hence particularly security-conscious when it comes to people scaling the barriers.
While unauthorized jumping is unwelcome, however, the Stratosphere is evidently opting for the "if you can't beat 'em" philosophy, having recently announced plans for its new SkyJump attraction. At $100 per person, the new $3.6-million Tower-top thrill ride will feature a controlled free fall that's said to be similar to skydiving or B.A.S.E. jumping. It's due to open mid-April.
