Baylor had five members of the 2013 team drafted in the third day of the MLB draft, along with two 2014 signees. The Bears have had multiple players picked in the draft for 15 of the last 16 years, and at least one player taken in the last 22 years. I've linked to each team's SB Nation site for future reference in parentheses next to the draft pick.
Dillon Newman went to the Houston Astros in the 16th round, 467th overall, and, as expected, was the first Bear taken in the draft. Newman is a junior, and as such is not a guarantee to sign with the Astros, as he could come back to anchor the Baylor rotation and improve his draft slot next year. Newman was the Bears' ace this past season, and was the former 49th round pick of the NY Mets. (Crawfish Boxes)
Cal Towey was picked by the Los Angeles Angels of Anaheim in the 17th round (517th overall) as a third baseman. A senior, Towey is a likely sign, and will probably start with their rookie league team in the Pioneer League, as the Angels are not currently affiliated with a short-season team. Towey walked 123 times in his Baylor career, putting him sixth on the all-time list. (Halos Heaven)
Max Garner, Baylor's closer-turned-starter, was taken in the 18th round by the Miami Marlins, rounding out a trio of Bears picked one round after the other. A senior, Garner will most likely sign with the Marlins and play for their short-season A team, the Batavia Muckdogs in the NY-Penn league. Garner earned 18 saves in his years with the Bears, tying him for fourth all-time. (Fish Stripes)
Darryn Sheppard, a 2014 outfield commit for the Bears, was drafted by the Texas Rangers with the 730th pick in the 24th round. Sheppard is almost certain to decline the draft bonus and play for the Bears starting this fall, and according to Jason Cole of Baseball Prospectus and LoneStarDugout "can really play center field." (Lone Star Ball)
Jake Miller was taken in the 27th round by the Arizona Diamondbacks, and the senior shortstop will most likely sign and report to Arizona's short-season team in Missoula. Miller was an honorable mention All-Big 12 selection this season. (AZ Snakepit).
Crayton Bare was picked one round later by the Los Angeles Dodgers with the 844th overall pick. The left-handed pitcher had 88 strikeouts in 87.2 innings of work with the Bears, and will most likely begin his professional career with the Dodgers' rookie league affiliate in Ogden. (True Blue LA)
Finally, a second Baylor commit, right-handed pitcher Josh Pettitte, son of New York Yankees' pitcher Andy Pettitte, was taken by the Yankees in the 37th round, with a largely symbolic pick. Despite being drafted by the organization that employs his father, both Pettittes emphasized the fact that Josh will be attending Baylor in the fall. The younger Pettitte pitched two no-hitters for Deer Park HS in his senior year. (Pinstriped Bible)
Good luck to all the Baylor draftees, and ODB wishes them well in the start of their pro careers!