It is easy enough to get updated tables like this:
(All these tables are updated to May 15, 2021):
Most Tests (120 and above)
Current players with the most Tests are Anderson (160) and Broad (146).
Another table which is easy to create:
Most Tests as Captain (40 and above):
Kohli is the only current player here. He has captained in 60 Tests and has equalled Dhoni (60). He overtook Ganguly (49), Gavaskar and Azharuddin (47) not long ago. Root is on 50.
But this one needs a little more work with Excel:
Most Tests NOT as Captain (90 and above):
Tendulkar and Kallis lead. The most by current players are 161 by Anderson and 146 by his team-mate Broad.
Now what about those who played the most Tests without ever captaining their sides (90 and above)?
Led by Anderson and Broad, who recently surpassed the long-standing record of Warne.
VVS Laxman (134) has the highest for India which will probably stand for a long time..
Other current players are Ishant Sharma (101) and NM Lyon (100).
Finally, those who played all their Tests as captains (all cases):
Most of them are from the olden days, except LK Germon (12). Perhaps there was an acute shortage of captaincy talent in New Zealand in the mid-90s. And there is Porterfield who captained Ireland in the only 3 Tests which they have played.
Note the 5 at the bottom who played only one Test, in which they were captain.
There are a fair number of the glorious amateurs and their counterparts like Vizianagaram.