To further explain what the other comments are saying: there are two main similarities/crossovers between the two shows:
1. Cast Members
Two of the main characters from the last couple seasons of Stargate SG-1 and two of the main characters from Farscape were portrayed by the same actors. Ben Browder portrays Cameron Mitchell in Stargate SG-1 and John Crichton in Farscape. Claudia Black portrays Vala Mal Doran in Stargate SG-1 and Aeryn Sun in Farscape.
Cameron and John are pretty similar, personality-wise. But Vala and Aeryn are pretty much opposites; Aeryn is a tough soldier and Vala is a wacky thief.
| Actor | Stargate Character | Farscape Character |
|---|---|---|
| Ben Browder | Cameron Mitchell | John Crichton |
| Claudia Black | Vala Mal Doran | Aeryn Sun |


2. "200" Parody
In Stargate SG-1 S10E6 "200", there is a bit where the cast mimics Farscape. If you are not familiar with the show, it just seems like they are making fun of a bunch of generic sci-fi tropes or something. But to anyone who knows the show, they are clearly parodying specific characters and speaking words from the fictional alien language in that show.
Another amusing detail is that rumor has it, Ben Browder and Claudia Black were supposed to reprise their Farscape roles as John Crichton and Aeryn Sun for this bit. But while Claudia Black did stick to the script, on the day of the shoot, Ben Browder and Michael Shanks supposedly decided it would be funnier if they switched. So, Michael Shanks ended up parodying John Crichton while Ben Browder parodied Stark.
| Actor | Stargate Character | Farscape parody Character |
|---|---|---|
| Ben Browder | Cameron Mitchell | Stark |
| Michael Shanks | Daniel Jackson | John Crichton |
| Amanda Tapping | Samantha Carter | Chiana |
| Claudia Black | Vala Mal Doran | Aeryn Sun |
| Christopher Judge | Teal'c | Ka D'Argo |
| some puppet | Thor | Rygel |
Bonus
And like with any sci-fi, there are a bunch of little overlaps between plot points and whatnot, such as:
