Are there set periods of time in which seasons start and end? In America, generally, TV shows begin in the Fall or the Summer. Many shows will start within a week or two of each other. Is the same true for anime? If not, what controls when anime seasons start/are released?
It's the same as Japanese Television seasons (or sometimes referred to as "cours"). There are 4 of them each year and each one lasts roughly 13 weeks. The Wikipedia page for Japanese Television Drama says:
Japan has four television seasons: Winter (January–March), Spring (April–June), Summer (July–September), and Autumn or Fall (October–December). Some series may start in another month though it may still be counted as a series of a specific season.
So while the seasons themselves have a fixed start and end, the shows themselves can sometimes start in the middle month of a season and thus spill over into multiple seasons (given that it's a 13 episode/1 cour show), but it is still considered part of the season that it started airing. There's obvious advantages to always starting at the beginning of a season, the main one being that shows lasting 12 or 13 episodes can continue to fill a time-slot throughout the calendar year without having breaks.
For example, here are the "Summer 2013" shows and their air-times:
- 07/01 22:25 (AT-X) - Recorder to Ransel Mi♪
- 07/01 25:00 (Tokyo MX) - Inu to Hasami wa Tsukaiyou
- 07/02 19:30 (AT-X) - BROTHERS CONFLICT
- 07/02 25:35 (TV Tokyo) - Senyuu. (Season 2)
- 07/02 25:40 (TV Tokyo) - Gifuu Doudou!! Naoe Kanetsugu -Maeda Keiji-gatari-
- 07/03 21:30 (AT-X) - Tamayura ～More Aggressive～
- 07/03 24:30 (Tokyo MX) - Free!
- 07/04 25:28 (TBS) - Tokurei Sochi Dantai Stella Jogakuin Koutou-ka C3-bu
- 07/04 25:35 (MBS) - Dangan Ronpa no Gakuen to Zetsubou no Koukousei The Animation
- 07/04 25:58 (TBS) - Rozen Maiden (New Series)
- 07/04 26:05 (MBS) - Ren-Ai Lab -Love Lab-
- 07/04 26:35 (MBS) - Senki Zesshou: Symphogear G
- 07/04 26:43 (Nippon TV) - Kitaku-bu Katsudou Kiroku
- 07/04 27:08 (ABC) - Servant x Service
- 07/05 22:30 (AT-X) - Rou-Kyuu-Bu! SS
- 07/06 20:30 (AT-X) - Kiniro Mosaic
- 07/06 20:30 (ABC) - Genei wo Kakeru Taiyou -il sole penetra le illusioni-
- 07/06 23:20 (Nico Nico Douga) - Fate/Kaleid Liner: Prism-Illya
- 07/06 25:00 (Tokyo MX) - Monogatari Series: Second Season
- 07/06 25:00 (Tokyo MX) - Genshiken Nidaime
- 07/06 25:30 (Tokyo MX) - Kami-sama no Inai Nichiyoubi
- 07/06 27:28 (MBS) - Fantasista Doll
- 07/07 20:30 (AT-X) - High School DxD NEW
- 07/07 22:27 (Tokyo MX) - Teekyuu (Season 2)
- 07/07 22:00 (Tokyo MX) - Uchouten Kazoku
- 07/07 22:30 (Tokyo MX) - Hakkenden -Touhou Hakken Ibun- (Season 2)
- 07/07 24:30 (TV Kanagawa) - Blood Lad
- 07/07 25:05 (TV Tokyo) - Makai Ouji: Devils and Realist
- 07/08 25:35 (TV Tokyo) - Kami Nomi zo Shiru Sekai -The World God Only Knows- (Season 3)
- 07/08 26:05 (TV Tokyo) - Watashi ga Motenai no wa dou Kangaete mo Omaera ga Warui!
- 07/11 24:45 (Fuji TV) - Gin no Saji: Silver Spoon
- 07/12 22:00 (BS Animax) - Hyperdimension Neptunia: The Animation
- 07/12 25:58 (Nippon TV) - Gatchaman Crowds
- 07/13 22:00 (Tokyo MX) - Futari wa Milky Holmes
- 07/13 23:30 (TV Tokyo) - Kimi no Iru Machi -A town where you live-
So, like you said, everything happens around the same time, the first week of July, then we have a few outliers that start during the second week. It's worth noting that Silver Spoon is only 11 episodes, and Hyperdimension Neptunia, Gatchaman Crowds, Futari wa Milky Holmes, and Kimi no Iru Machi are all 12 episodes, so they'd end right at the end of the season.
The real outliers from last season, Spring 2013 (though some sites attach these 2 shows to the Summer 2013 season), would be:
- 06/08 23:45 (NHK-BS Premium) - Kingdom 2
- 06/14 17:55 (Disney XD) - Yuuto-kun ga Iku
In some cases, certain channels will start a show in the middle or near the end of a season, sometimes because of a timeslot that needs to be filled. Kingdom 2 is a 39 episode historic drama on a pay satellite channel that doesn't have any other anime, and the other is a 5 minute-per-episode young children's after school show. These are shows that are typically outside of the usual late-night anime demographics.
See also this question: What defines one "season" of anime?