Favorites... can be favorites because of usefulness, liking the unit for reasons besides pure team usefulness, or a combo of both... At least for me.
Fire:
* Bestie - has been extremely useful to me since I got her, and I wanted her ever since seeing her art
* Ruby - ...I don't really have many fire units... Ruby makes 3 turning Terminus fun, though, and she was my first unit (that wasn't Karl XD) with a BB fill on Spark effect on her LS.
Water:
* Quartz - Surfs on a sea skeleton and just seems like a badass. If only his conversion buff wasn't so annoying to have compared to any other conversion to attack...
* Medina - Instant fill should not be overlooked in its usefulness, especially with her BB-fill-when-hit. She also was my first 6* unit, and once I got her to 6* , I finally was able to take off and really enjoy playing the game without being concerned about saving BB's for the boss of a level.
Earth:
* Edea - My first 7* mitigator, and a very convenient one at that. Even summoning 4 oracle Edea's in a stretch of 6 Medal Rush gate summons can't make me sour TOO much on her. ...does on that gate, though...
* Elaina - Loved her design from the first I saw her. She also was my backup healer for a while behind Ivris, being my second healing unit that I ever summoned. It's really sad that they "buffed" her with stuff that... still leaves her very underwhelming, compared to pretty much everyone else.
Electric:
* Shera - My first mitigator, and one of my first summons overall in this game. Love her design and story/personality, as well as her usefulness. Right now, she may be one of my favorite units overall to use.
* Rhoa - Another unit who I love for design, story/personality, and usefulness. He also was my first good 7* capable spark buffer.
Light:
* Will - So much utility, and he's got an awesome backstory, too. Still like to use him even when another unit on my team carries a higher BB attack buff, sometimes.
* Nemethgear - I AM GUNDAM. (also, Lilith 7* is not out yet, for me to try out and see if she'll be as fun to use as I think she might be)
Dark:
* Zenia - The unit I wanted most in this game, from the moment I first saw her. It didn't hurt that she also was very powerful to use. Sadly, I finally summoned her by a time when more units came along to make her less useful, but even so... she still is my favorite. I kinda wish her 7* art was closer in design/quality to her 6* art, though...
* Ivris - My first summon gate healer, and a very useful one at that early in my days as a summoner. She's less used now, but... I still tend to find her more useful to my teams than anyone on reddit ever seems to find her on theirs... Must be my weird assortment of units. XD
And beyond all that... Cyan and Reud are the two units I do not have, that I'd really love to get, because I think their designs are cool. Reud also seems like he'd be incredibly useful to use (might just try and slot in Cyan for fun, if I get her, just as a sub, but she probably has less use for me).