Visitors can be randomly encountered after certain levels and clicking on them in the command center unlocks a pet. This is the list I made when I went through the game on a clean file:
1- ?
2- Rochelle Met/Farnsworth
3- Ned Shortwave/Buzz Rainbow (This pet is needed for an achievement)
Rose Chevelair/Snap (Unlocked for me after saving the robots on a second try)
4- Sam Onestar/Banya
5- ?
6- Clamp Snapjaw/Ludwig
7- ?
8- ?
9- ?
10- Moltarr/Seleck
11- Tanya Goodson/Trip Sparkles
12- Trent Sylex/Scribbles
13- Vera Drax/Smax Immortal
14- ?
15- ?
16- ?
17- ?
18- ?
19- ?
20- Marquis Ice/Hermes
21- Glenda Royal/Zip
22- Omid/Tater Tot
23- ?
24- Logan Clone 3/Maygel Mode
25- Kat Duran/Scorch
26- ?
27- ?
28- ?
29- ?
30- Trigger Newman/Homan