The Inhumans didn't
At least, the ones under Jiaying (played by Dichen Lachman) in the Afterlife didn't. I would think those under the dominion of the Royal Family in Attilan would be leery of it as well.
Once Robert Gonzales (Edward J. Olmos) broached the subject in his negotiations with Jiaying, it didn't take long for the Inhuman matron of Lai Xi to register her displeasure. She broke a Terrigen Crystal laced with Diviner materials to see if the erstwhile director and current board member of S.H.I.E.L.D. might have some Inhuman in him. He didn't.
And, with his death, she set in motion events that will (apparently) lead to a war between the Inhumans and the now-combined forces of S.H.I.E.L.D. (I wonder if Phil Coulson (Clark Gregg) will have Nick Fury (Samuel L. Jackson) send that helicarrier back to him...).
Dr. Calvin Zabo / Mr. Hyde (Kyle MacLachlan)
seems to resent being on it
And, having his daughter, Daisy Johnson / Skye (Chloe Bennet), on it really rankled him. His short-lived band of S.H.I.E.L.D. antagonists: Karla Faye Gideon (Drea de Matteo), Wendell Levi (Ric Sarabia), Francis Noche (Geo Corvera) & David Angar the Screamer (Jeff Daniel Phillips); all seemed to share his concern.
Professor Elliot Randolph / The Berzerker (Peter MacNicol), asked, and was granted his request by Coulson, to be left out of any records that would identify him as an Aesgardian to maintain his privacy. So, early on, we see that Phil understands and has empathy with those who don't want to be Indexed.
Some, we don't know about
Donnie Gill / Blizzard (Dylan Minnette) is a good-hearted super genius in the vein of Leo Fitz (Iain De Caestecker) who got caught up in a Hydra scheme put together by Ian Quinn (David Conrad) and fellow student, Seth Dormer (Daniel Zovatto) and ends up almost killed (Seth was killed) when he attempted to do the right thing and shut off his ice-making device. Unfortunately, the device back-fed its energy into his body and gave him the same abilities as the machine - within his physical person. He's probably not happy with being on the Index, but he's way too busy just staying off the grid and out of anyone's sight... particularly those who would want to lock him up (literally or figuratively).
Carl "Crusher" Creel / Absorbing Man (Brian Patrick Wade) is probably more interested in getting out of General Glenn Talbot's generous lodging facility (probably at some super-secure military base) than having a notion of getting off some idiotic "Index". Odd that the Wiki page for him in the MCU shows him as "deceased"... Coulson left him in a van in suspended animation for Talbot to cart away.
Some probably don't really care
I'm sure Lady Sif (Jaimie Alexander) has her entry on the Index. Thor (Chris Hemsworth) does. I'm guessing Fandral (Josh Dallas), Hogun (Tadanobu Asano) and Volstagg (Ray Stevenson) all have at least a mention from their foray in New Mexico backing up Thor. But, I doubt they really care, much, about some paltry list in human hands.
Loki (Tom Hiddleston) for sure will be on it. I doubt he worries much about what the miniscule humans are scurrying around about to maintain control of their pathetic little lives. The same could be said for Lorelei (Elena Satine).
Odin (Sir Anthony Hopkins) and Frigga (Rene Russo)? I'm not sure... they've not made an appearance on earth... er... Midgard, but I am sure historians within S.H.I.E.L.D., once they realized Thor was an actual being in their universe, sorted any number of Aesgardians into their cute, little list.
Kree Champion Vin-Tak (Eddie McClintock) won't remember he was here or that Coulson and crew now have record of his visit. His incursion onto the third rock likely opened up a whole new subsection of the Index just waiting to be populated. Maybe they logged him in the same category with that blue "John Doe" we saw at the Guest House.
I'm sure the rest of the Avengers are on the Index - whether they know it or not is another question...
Volunteer Firemen Tony Diaz (Vincent Laresca), Adam Cross (Rick Gifford) and Baker (Robert Maffia) who all were stricken with that Chitauri virus from contact with the souvenir helmet they approrpiated after the Battle of New York won't care... they all died. But, that does lead me to wonder if there might be some aftereffect for Agent Jemma Simmons (Elizabeth Henstridge) who also contracted the virus but was ultimately cured through her and Fitz's frantic efforts. Being cured doesn't wipe the antibodies her system developed (or that were injected into her) and could lead to a riveting story line later on in the series.
Hydra and its agents probably assume S.H.I.E.L.D. has files on any of them that have become known to S.H.I.E.L.D. in any way. Index or catalogue or whatever... Once they take down S.H.I.E.L.D., they won't have to worry about any of that clueless organization's records. They'll have them in hand.
But, some didn't seem to mind
Mike Peterson / Deathlok (J. August Richards) volunteered to go on the Index as a way to atone for his earlier misdeeds. He is happy and ready to serve any capacity S.H.I.E.L.D. requires loyally and determinedly.
Skye, for her part, allowed Coulson to Index her; although, she appeared to have some reservations. She still trusts Phil and his merry band of 0-8-4 hunters and will serve as needed (unless her mom grounds her and sends her to her cabin to cool off).
Phil Coulson put himself on the Index - he is aware of his being injected with the GH-325 serum and isn't sure how it will ultimately affect him. My guess? If he gets exposed to Terrigen Mists, he will transition. Then, he'll have to update his Index entry to account for his new physical being.
Update (5/14/15): Well, after the Season 2 Finale, we now know that Phil is not Inhuman and is not immune to the effects of the Diviner. Mack had to chop off his arm to keep the contaminated Terrigen Crystal from charcoalizing the rest of him out of existence.
But, then, I'm guessing all S.H.I.E.L.D. agents are Indexed so that their specific skill sets are available for utilization as needed.
The Index is, likely, quite huge
Some go on it willingly (S.H.I.E.L.D. and its agents), some don't realize they're on it or, if they do, don't consider it a threat to them and some feel the intrusion such a list is making in their lives pertaining to their privacy and their freedom and liberties and aren't very happy about it.
The issue, really, isn't on being on some sort of List. The issue is, Who Has Access To That List, and Who Can Control What Happens to Individuals On That List. There are a lot of multi-billionaires in the world that like for nothing less than having every available resource at their beck-and-call.
Not all billionaires are dangerous this way... but, all it takes is one!
- If they need a great jeweler to craft an unimaginable necklace to court the woman of his dreams? That jeweler is on file and his assistant has immediate access to call in the job.
- If they need an incredible home built, all the best contractors are right there... on their list.
- If they need someone to obtain information on a rival to gain leverage in the market or in a deal?
Where's that Index? Who controls it? How much would it cost to get information out of it?
Someone, somewhere who can be bought, cajoled or otherwise coerced into getting that information is at their disposal. All it takes is a little effort. And, maybe, a little money.
Aesgardians don't care. They are out of reach of mere mortals.
Hydra doesn't care... most of them have an employment "incentives program", anyway. And, once they get their hands on the Index, it won't matter, anymore.
Would you want to be on that Index? Would you know for a fact that you (and your family and friends) were safe if you were Indexed?