Romantic History

I find the history of "love" and "relationships" in the Sonic series an oddity.

History

1990s

So in the beginning of the Sonic series Sonic had plenty of love interests, or plans for ones.

In Adventures of Sonic the Hedgehog, the first cartoon, Sonic met girls frequently.

"'Your always saying how you like babes.'
'I MEANT babes as in 'girls' not babes as in 'babies'" 
--Sonic and Tails when on a babysitting job.

There were many including: Miss Possum; the Merhog girl; and most interesting, Breezie, who Sonic completely fell for until he learned her true nature.

None of these characters had a major role in the series as a whole. Conversely, the "Saturday Morning" Sonic the Hedgehog show introduced Sally, who appeared alongside Sonic in the show more than Tails. The character had been planned since the beginning of the first game, based on one of Sonic's animal friends (the animals that pop out of the robots in Sonic 1). In the 90s, Sally would be Sonic's "officially unofficial" girlfriend due to her lasting impression from the show and her lasting appearance in the Archie Comics.

In the original Sonic the Hedgehog video game, there were plans for a blonde human girl named Madonna who would have been Sonic's girlfriend. Sometime later Amy Rose appeared in Sonic CD. The character had already made an appearance in comics in Japan. In America, to stick to "Western canon" and support the Sat Am cartoon, they called the character Sally instead of introducing her as a new character (although she would appear as herself in the comics).

She would later appear in the US as Amy (or Rosy?) in lesser-known Sonic Drift 2 and Sonic the Fighters.

At one point, the concept of Sat Am was supposed to make it into a game, and likewise establish Sally as Sonic's girlfriend, but this idea was scrapped. In it's place the nearly-made Sonic X-treme would have made Sonic's girlfriend a manx cat, Tiara Boobowski.

Early material referred to her as a princess, but the more recent plans instead made her the daughter of a professor. Her involvement varied, too. In one case, the plot would have had to do with a date between Sonic and Tiara, while another had them work together when infected with a deadly virus. Tiara was supposed to be "Sonic's Match," but she, like the game, was cancelled.

The 90s also saw the introduction of Sara, a cat-girl who liked Sonic in a way similar to Amy. In Sonic Underground, it was Sonic's sister, Sonia, who had relationships (including an ex-fiance). Meanwhile a some romance had brewed in the comics, like with Knuckles and Julie-Su, although Sonic and Sally were arguably still the focus. Over in the UK, Sonic the Comic's main possibility was Sonic and Amy (with a completely different personality) until the series' end.    

2000s

Although Sonic and other characters had relationships in "other media," the only real love interest for Sonic in the games was Amy. So when Sonic Adventure revived the series, Amy made a new appearance. Redesigned and older, Amy was now the primary love interest. She was still younger than Sonic, though, and immature, so Sonic did not act interested.

As more characters appeared, the games started to take on an implying role, rather than officially confirming whether characters like each other.

Although the next cartoon, Sonic X, would generally continue this trend, the couples were more obvious. Tails nearly told Cosmo he thought she was beautiful, Sonic gave Amy a rose and began calling her "Ames" (it's thought that the two were dating after season 2), and even Chris was slated with his old friend, Helen.

Meanwhile Sonic's love-life in the comics was crazy. In the real world, creative differences caused confusion in the comics. He was dating Sally, then they broke up (SLAP). He was supposed to date Amy, but instead ended up with character called Fiona. Somewhere in there he kissed Bunnie, confusing readers, and he also knew a girl named Mina. Other characters had their own break-ups and heart-aches, too. Tails liked Fiona Fox, who Sonic was dating! And she ditches him for anther guy (sort of).

The first game to put ideas of "love" into Sonic's plot was Sonic the Hedgehog (2006), where Sonic rescued a princess. A human girl named Elise, she began to grow feelings for the hedgehog. There was even a point where Sonic had to choose if he liked Amy or Elise. Unfortunately, this had no impact on the rest of the game and their relationship was rather shallow. The game was very poorly received, and the Last Story where Elise kisses Sonic heavily criticized.

Most games would stick to the original implying plan, usually relying on "ship-tease." Certain "couples" would often be paired together in game plots. Sometimes other characters would call them out on this or else one of the two would "tease" the other.

However, Sonic Unleashed brought "Sonamy" back as a possibility. Unlike before, Sonic did not seem annoyed by Amy and there was a point where Sonic could refute or accept a going on a date with her. Maybe following up to this, Amy claims Sonic was late for their date at the end of Sonic and the Black Knight. In Sonic Chronicles, the player has a choice to have Sonic bond with Amy or ignore and mock her.

2010s

By the time of Free Riders and Generations, though, the "Sonamy relationship" returned to it's previous status of Amy liking Sonic and Sonic avoiding her.

The newest TV show, Sonic Boom, takes place in an alternate world. Like the games it would often suggest couples, mainly Sonic and Amy and occasionally other characters like Knuckles or Sticks. In this series, Amy took on a more mature attitude and kept her crush on Sonic a secret. It's also fairly obvious Sonic may have a crush on her too, but neither of them take action beyond a few words and (even in an alternate series) the characters go nowhere.         

The characters of the Archie comics had straightened their relationships out...until several dark turns pulled them apart. Due to outside forces, the comic was rebooted and those "dark turns" (and other stories) were lost.

After the reboot, Sega added more rules to the comic, among them was a rule that Sonic and other game characters could not be in a relationship with each other or with comic characters. As a result, those characters were limited to suggested relationships similar to the games. Comic characters, however, were free to date each other, and the series would introduce a few new couples, as well as keeping together long-time Bunnie and Antoine.

Pre-Reboot Bunnie and Ant

Sonic Forces saw the return of many characters, but the script didn't make room for flirting. Since Blaze was back in her dimension and Rouge was more likely to be around Shadow or Knuckles, Amy was the only girl who could have filled the role as Sonic's love interest (unless you make the avatar a girl and ship them?). Sonic Mania didn't even include Amy as a possible player, although she had a cameo and a part in an animated short.   

The tail end of the decade also introduced the IDW comics in place of Archie, but it with the rate it's gone as far as relationships, you could probably ship any of the characters with any of the other characters.

Reasons Sega's Been Restricting Relationships and Other Theories 

• One obvious reason is Sonic 06. The game did bad, so they don't want to do something wrong and repeat their mistakes.
• They don't want to upset a portion of fans. Having Silver ask out Blaze, for example, would infuriate Sonaze (Sonic-Blaze) fans (ME). 
• The comics became too confusing. They added characters beyond the games and complicated the histories between them, making it hard for new readers to understand. 
• Pender's Lawsuit. Although the conflict was over characters, they put more strict rules on the comics to prevent similar occurrences. While this may have seemed exclusive to the comics, it's possible Sega puts these same rules on Sonic Boom and the games.
• People take things too seriously/find ways to make things worse than they are. Being a video game aimed for younger audiences, Sega probably doesn't want phrases to be taken out of context (PINGAS) or taken the wrong way (like Sonic and Elise).   
• A change in cartoons over time (plenty of "modern" shows avoid "real" couples, like Spongebob). 
• It's a series targeted for boys. And they typically don't like romance. 
• Change in Voice Actors--this is a stretch, but going from the 4kids actors (fans at least agree on "Best Amy") to the current group (with the joked "Minnie Mouse" Amy) probably didn't help. 

It seems like over the years, less and less is allowed. For the most part, any "ship" remains undeveloped beyond it's origins, and it's kind of disappointing. I understand that that's not the main focus of the games. But with a series so dependent on characters, it would make sense to connect the games in a way that an old fashioned "Eggman's taking over" story could not. One of Sonic's many advantages over Mario is his ability to change over time, but in this case Sega's failed to take action. If it means the story will be better, wouldn't it be worth the risk?

Happy Valentine's Day