With Robert and Renly all dead, are there any male Baratheons left other than Stannis? I'm not looking for bastards, but actual Baratheons.
Legit ones, no. Bastards, 16 total, if we are to believe Maggy the Frog and not all of them in King's Landing.
Here are the ones mentioned in the books some of which may or may not be verified.
Mya Stone--she's the bastard with the burro, and Sansa's guide to the Eyrie. According to the books she's Robert's first off of a commoner. An open secret, but she herself might not know. Female, so she doesn't meet your male line criteria.
Edric Storm--conceived with a noblewoman, Delena Florent, this child is acknowledged as a bastard of the king's. The story goes that he was conceived in Stannis' marriage bed, on the day of Stannis' wedding, by Robert with a cousin of Stannis' bride. Stannis saw this as an affront (as one would) and sent him off to be fostered at Renly's. Later, the boy is with Stannis and company. The Red Woman wants to sacrifice him because he has the blood of a King, and Davos smuggles him out. Stannis isn't happy, but also seems a bit relieved that the choice has been taken out of his hands. (I believe he's only in the books, not on the show).
Gendry Waters-- The blacksmith, travels with Arya, meets with Ned Stark. Escapes with the Night's Watch from King's Landing. If you don't know him you haven't read the books or seen the TV show.
Bella--mentioned in passing, a blink-and-you'll miss it reference, when they pass through the Stony Sept with the Brotherhood without banners. She and Gendry actually meet. She's a prostitute whose mother was a prostitute favored by Robert, and she has the trademark coal black hair. Gendry passes on a chance for sex with her...which is good...(This was in the books, but I don't know that it was on the show).
There are other bastards, but many of them were likely ordered killed by Cersei. Pretty much, if they were in King's Landing where she could get her minions to off them they are likely dead (like Barra, the child less than a year old that Ned Stark visits). Gendry escapes, but most probably did not. Robert had so many though, it's hard to say if we have met all the living ones. The possibility of another male bastard of Roberts is not totally unlikely.
Legitimately, there's Shireen born of Stannis, who though dead in the TV series, is not in the books, and is female. He's unlikely to have a bastard. Unless you count his shadow-child, and I don't. (Stannis is also dead in the TV series, but alive in the books).
Renly wasn't into the ladies so he is unlikely to have any issue.
Conclusion: If there are any males left of the line, they are illegitimate and they are Robert's. I've listed all that I recall from the books (and I think there's an unnamed set of twins, and maybe 9 or 10 others). In the books, not all of Cersei's kids are dead either--Tommen and Myrcella are still alive. Although Tommen isn't actually Robert's kid, he technically has the last name of Baratheon.
Before we move on, remember, please don't confuse show and book facts: in the show, Stannis Baratheon and his entire family is wiped out, in the books, he, Selyse and Shireen are alive and well.
As I pointed out in my other answer, it depends on the perspective you take
Shireen is the heir as she is the only surviving legitimate family member of Robert Baratheon's.
Check out this awesome line from Stannis himself in his pre-released chapter from the forthcoming Winds of Winter book (speaking to Ser Justin Massey):
"It may be that we shall lose this battle," the king said grimly. "In Braavos you may hear that I am dead. It may even be true. You shall find my sellswords nonetheless."
The knight hesitated. "Your Grace, if you are dead — "
" — you will avenge my death, and seat my daughter on the Iron Throne. Or die in the attempt."
-A Song of Ice and Fire: Book Six - The Winds of Winter, Theon I.
This guy's dedicated to the end.
Failing Shireen, it will fall down to one of Robert's bastards:
- Edric Storm
- Mya Stone
- If someone decides to acknowledge him, he'd be at the top
Most likely, Gendry will be though, given that he's the only known or heard of offspring of Robert's, given that Renly died without issue and Stannis' entire clan has died, including poor Shireen.
The truth is that given the show's treatment of this entire lineage, it seems like they want us to believe they are all dead, buried and to be forgotten. In reality though, if you were to truly trace the family's heritage back, it would end with Sam Tarly (if you take Dany's side) or Cersei Lannister and whatever child she's bearing (if you take Cersei's side).