Carrie/JT

Taylor Swift - Coldplay
Taylor Swift - Eminem

Miley/Adele twerk to the death

Rihanna/Bey

EDIT:
RihannaLoverrr beat me to it

2NE1/Lady Gaga
Bigbang/ Justin Timberlake
Rihanna/Gaga
Taylor Swift/Harry Styles

This would be a mess

Madonna & Rihanna
Afrojack and Eva Simons (again)
Britney and Katy

Honestly any big name collab for Gaga to get back in the public's good graces

But I would personally love:
Shakira & Gaga
Adele & Gaga
Kendrick Lamar & Gaga (yes I know it didn't work out the first time)
Frank Ocean & Gaga
Lana & Gaga
Lana & Beyonce
Miguel & Bey
Kanye & Gaga

If gaga & xtina did a collab anything is possible

Britney & Xtina
Madonna & Rihanna
Rihanna & Miley

For some reason, Lana and Beyoncé.

Gaga with the following, all seperate songs:

Madonna
Bruce Springsteen
The Rolling Stones
Justin Timberlake
Eminem
Ke$ha

Lana & Madonna. This would slay

Gaga / Ke$ha
Gaga / Nicki
Gaga / Kylie
Kylie / Britney
Gaga / Britney (most likely happening )
Ke$ha / Nicki
Ke$ha / iggy Azalea

Britney and Kylie
Britney and Gwen
Kylie and Madonna

Gaga and Nicki
Gaga and Madonna (impossible, unfortunately).

Ke$ha/Katy
Hayley Williams/Katy

Out of these, that could be released:

Gaga feat. Azealia
Kendrick feat. Gaga