Sheldon Cooper and Leonard Hofstadter are best friends. The two genius physicists are socially clumsy and awkward, making it hard for them to make new acquaintances, hence why they became friends in the first place.
Still, they aren't opposed to making new friends, especially by the time The Big Bang Theory ends and they are at their most sociable. In fact, several television characters would find it easy to get along with Sheldon and Leonard, and a few might even become their friends. It wouldn't be easy because Sheldon is notoriously difficult, but they'd find a way to make it work.
Spencer Reid - Criminal Minds
Sheldon and Leonard usually have trouble making friends with people less intellectually gifted than them. It makes sense they should gravitate toward equally intelligent folks. Spencer Reid from Criminal Minds would perhaps get along better with Leonard than Sheldon, but the three would still get close enough to consider each other friends.
Spencer would find common ground with Sheldon and Leonard due to their troubled childhoods and wide range of interests. For once, Spencer would talk about something he likes without having other people react indifferently or confused. Spencer almost got killed several times throughout Criminal Minds, and his stories would fascinate Leonard and terrify Sheldon.
Abed Nadir - Community
Few characters are as pop-culture savvy as Abed Nadir from Community. He is as emotionally and socially inept as Sheldon and Leonard, which would make their initial interactions awkward and clumsy. The three would eventually find common ground through their shared love of everything pop culture, forming a feeble bond that would strengthen over time.
Like most other people, Abed would probably get along with Leonard and learn how to tolerate Sheldon. Still, the genius Dr. Cooper has a way of sneaking into other people's hearts, and Abed wouldn't be the exception, even if befriending him would take considerable time.
Seth Cohen - The O.C.
And speaking of The O.C., Seth was famous for his love of comic books, superheroes, and Chrismukkah.
Sarcastic and smart, Seth would Leonard in annoying Sheldon. His self-deprecating humor would go a long way to endear him to Leonard and Sheldon, while his good looks would quickly earn him the girls' appreciation. Seth would have a hard time dealing with Sheldon, but his liking of Leonard and even Raj and Howard would help him put up with the difficult Dr. Cooper.
Cisco Ramon - The Flash
Sheldon and Leonard love superheroes, so of course, they would jump at the chance to meet and befriend one in real life. Sheldon might even try to tone down his more Sheldon-y way if it meant befriending one of the Flash's best friends. Cisco would appreciate their efforts, even if he found them slightly tiresome.
Cisco's love for comic books and heroes would go a long way with the notoriously pop-culture-obsessed Sheldon and Leonard. All three would spend hours talking about Barry's exploits and how they compare to other comic book speedsters like Quicksilver and Makkari.
Dexter - Dexter's Laboratory
As children, Leonard and Sheldon longed for friends to who they could relate without fear of bullying. However, even they would've had trouble befriending Dexter, one of television's smartest child geniuses.
As adults, they would try to take Dexter under their wing and guide him to the right path, not knowing that Dexter's pride is equal and perhaps greater than theirs. Still, the young genius would appreciate the company of two people as intelligent as him and try to pull them into his disastrous creations. His laboratory would also dazzle Sheldon and Leonard, and all three would spend hours in it, creating one wild device after the other.
Frasier & Niles Crane - Frasier
The Crane brothers have a similar relationship to Sheldon and Leonard. They might not be geniuses, but they are remarkably intelligent and cultured. Frasier and Niles are also very stubborn, prideful, and snobby, qualities that would further complicate their relationship with The Big Bang's geniuses.
Still, all four could form a feeble but genuine friendship. The Cranes would drive Sheldon nuts and vice versa, but they'd still draw pleasure from their highly intellectual conversations. Sheldon would also finally have two worthy opponents in chess, much to poor Leonard's dismay.
Jared Dunn - Silicon Valley
Jared is sweet, loyal, and delightfully weird. His name is actually Donald, but he went with Jared because Gavin called him so. Jared is one of the most intelligent characters in Silicon Valley and can also get remarkably dark at times, giving him an edge.
Sheldon and Leonard would find Jared curious but endearing. They would see him as someone as clumsy and possibly more awkward than them, compelling them to befriend him. Jared might not have a genius intellect like them, but he would give them his undying loyalty, and that's more important.
Velma Dinkley - Scooby-Doo
Velma is extremely intelligent and highly logical, making her the female Sheldon in many ways. Velma isn't socially awkward, though, so it's more likely that she'd become friends with the girls. Indeed, Velma would get along famously with Amy and Bernadette.
Still, Velma's Sherlock Holmes-like personality would make her fascinating for someone like Sheldon. Leonard would also find her intriguing and enjoy listening to her crime-solving stories. For her part, Velma would find great value in the guys' physics expertise, forming a connection of the mind.
Wesley Crusher - Star Trek: The Next Generation
It's no secret that Sheldon and Leonard adore Star Trek. Sheldon, in particular, loves the character of Wesley Crusher, who he related to as a child for obvious reasons. The Big Bang Theory shows Sheldon becoming friends with the actor who played Wesley, Wil Wheaton, but he would absolutely also get along with the actual Wesley Crusher.
Sheldon and Leonard would probably annoy Wesley with their many, many, many questions about space, the final frontier. Still, the three would ultimately take Wesley under their wing, although the young Crusher would probably end up being a teacher to the two physicists.
Ross Geller - Friends
Friends' most infamous character would get along famously with Sheldon and Leonard. For starters, all three share the same ion for knowledge, love correcting others and always being right, and have PhDs in fields other people consider confusing or boring.
Like the Big Bang guys, Ross often found himself in sticky situations in Friends, mainly because of his social inadequacy. The three guys would have a ton of problems, though, especially because Sheldon and Ross are so stubborn. However, they'd eventually make their friendship work, although they would never be particularly close.