Good question. With primogeniture the usual fate of a rich family is that the money descends through a daughter sooner or later, and the surname is carried on by unrecorded landless younger sons of younger sons. So you end up with a lot of people with the name but no paper trail. Until one of them emigrates, and then the ancestry miraculously appears to the writer of the family book.
But there are some families that have defied nature so far. The trick with most of them would be to trace the living descendants - if there's no immigrant, they aren't usually on WikiTree.
1. The Somersets must be clear winners on paper trail - an unimpeachable line back to the husband of the heiress of Anjou. Of course we can't be confident against NPEs.
2. Warrens - it's complicated
3. MacDonalds. It's generally accepted that they go back to GilleBride. They have a big DNA project that I haven't seen, but their expert is on WikiTree. The clan head has a trail presumably.
Berkeleys]. MedLands has citations back to Ealdnoth the Staller, d 1068. WikiTree takes the line back into horned-helmet territory. The last Earl died in 1942. Dunno who's still living.
Major cadet branch, at Beverstone, MRCA around 1350. This descended to a John, who I've just connected up. He went bust and sold up around 1600, then emigrated to Virginia and got killed by Indians. He left a son in Virginia, Maurice Berkeley-178. Living y-descendants aren't ruled out. Maurice had a bunch of brothers who nobody seems interested in.
5. There was another Berkeley family, of Dursley, going back to the Conquest ish and presumably the ancestors of the Scottish Barclays.
6. Harcourts. MedLands goes back to Torf the great-great-grandfather of Ivo, about 1000. WikiTree squeezes in a couple of extra generations and then goes all the way back to Gandalf and Frodo. Line descends to Harcourt-396 d 1565 who had 6 sons, but WikiTree only follows the daughter, down to a gateway immigrant.
7. Fiennes. Back to the time of the Conquest on MedLands, or 7 generations earlier on WikiTree. MedLands doesn't have the crucial Giles, but sources are said to exist. Not all modern Fienneses are really Fienneses, but some may be.
8. Disappointing near miss, by only about 40 years - the last Earl Fitzwilliam had a straightforward descent from Ketelborn [[UNKNOWN-101801]], b. bef 1100. But the titles are now extinct, which means there's no male line from the 1st Baron. All the early Yorkshire landed branches died out. There are still Fitzwilliams on the electoral roll. However, there was an Irish Fitzwilliam family, not known to be related, and now we may never know.
9. Still going strong, with a title that should be extinct but isn't, just goes to show, the Talbot Earls of Shrewsbury. MedLands doesn't take them further back than Richard [[Talbot-541]] d abt 1175. The recent earls aren't on WikiTree, but I'll add them. Apparently most of the earls have disappeared from the crypt. Make what you like of that. Doubt if they'll get tested in case they turn out to be reptilians. Supposedly no male-line descendants of the 1st Earl, but there are lots of Talbots around.
Off the top of my head, some other long-lived heiress-free families with known early origins, worth checking for living descendants as the names are common enough - Fitzgerald, Burke, Mainwaring, Montfort, Graham, Percy (Kildale cadet branch - the line to the earls had an heiress), Neville of Raby, Harrington, Clifford, Marshall, Bruce (English branches), Poyntz, Mohaut/Maude, etc.
A lot of questions could be answered by a Leicester-style approach - trace the key testees, locate them, pay for the tests. But the key testees are needles in haystacks and just waiting for them to turn up won't get far. And we haven't got forever - Michael Ibsen's kids wouldn't be any use.