Burn Notice (USA) June 4
The title refers to the burn notices issued by intelligence agencies to discredit or announce the dismissal of agents or sources who are considered to have become unreliable. When a spy is burned, they are wiped off the "grid". According to the narration during the opening credits, the burned spy has no prior work history, no money; basically no identity. The television series is a first-person narrative (including frequent voice-overs providing nuggets of exposition) from the viewpoint of covert-operations agent Michael Westen, played by Jeffrey Donovan.
After fleeing a Nigerian operation blown apart by the sudden and unexplained non-cooperation of his U.S. contact, Westen finds himself in his hometown of Miami, Florida, attended to by his ex-girlfriend, Fiona Glenanne, but abandoned by all his normal intelligence contacts, under continuous surveillance with his personal assets frozen. Extraordinary efforts to reach his U.S. government handler eventually yield only a grudging admission that someone powerful wants him "on ice" in Miami; if he leaves the city he will "heat up fast", i.e., he will be hunted down and taken into custody, whereas by staying there he can remain relatively free. Consumed by the desire to find out why he has been burned, and by whom, Westen goes to work as an unlicensed private investigator/spy/soldier of fortune for anyone in town who can pay him any money in order to fund his personal investigation into his own situation as a blacklisted agent.
Eli Stone (ABC) June 20
The show starred Jonny Lee Miller in the title role of attorney Eli Stone. In the first episode, Stone is discovered to have an inoperable brain aneurysm which is causing hallucinations. His acupuncturist, Dr. Chen, suggests that his hallucinations are actually divinely inspired visions of the future. These visions often foreshadowed future cases and events, including an impending earthquake.
Cleaner (A&E) June 23
William Banks, played by Benjamin Bratt, is a drug addict. With the birth of Lula, his daughter, William makes a deal with God arguing, if he is given a second chance, he will end his drug abuse and help others to end their addictions to sex, drugs, and gambling. William Banks and a small team of recovering addicts work to help others in recovering from their addictions. Banks and his team will resort to unethical and illegal tactics in order to end their clients' addictions.
Listener (NBC) June 4
he Listener is a Canadian supernatural drama about a young paramedic named Toby Logan (Craig Olejnik) with the ability to listen to people's most intimate thoughts. Aided by his partner Osman Bey (Enis Esmer), Toby Logan is a 28-year-old paramedic who did not know his parents and grew up in foster homes. Until now Toby has kept his ability secret and the only one he has shared it with is his old counselor and confidant, Dr. Ray Mercer (Colm Feore). While he crosses the city of Toronto in his ambulance with his partner Oz, Toby tries to help persons in crisis and on the way treat his own wounds. With the help of Detective Marks (Lisa Marcos) and his ex-girlfriend Olivia (Myléne Dinh-Robic), an E.R doctor, Toby realizes that his gift can serve to help other people.
Survive This (CN) June 17
On this show, Les Stroud takes eight teenagers into the wild to teach them how to survive.
Merlin (NBC) June 21
Merlin is a British television drama series that began in 2008. It is loosely based on the Arthurian legends of the mythical wizard Merlin and his relationship with Prince Arthur, but differs significantly from traditional versions of the myth. Produced by independent production company Shine Limited for BBC One, the programme was designed to run in the same Saturday evening family drama slot as other UK series such as Doctor Who and Robin Hood.
(I was kind of rushing to get this done so all synopsis quotes above are taken from wikipedia.)