Same song different artist. Which ones do you love? LP

I probably should have mentioned "You Got What it Takes (to Take What I Got)" by Joe Tex, later covered as a duet by Marti Jones and her husband, Don Dixon. My wife and I used the latter version as our first dance.

The Feelies used to end their live shows with great cover songs - Everybody's Got Something to Hide but Me and My Monkey (Beatles), King's Lead Hat (Brian Eno), All Tomorrow's Parties (Velvet Underground). Etc.

A few stealth covers from Cyndi Lauper - "Money Changes Everything", covering The Brains, and "All Through the Night" her cover of Jules Shear.

Strange variation 1:  "World Turning", Lindsey Buckingham and Christine McVie's re-work of Peter Green's "World Keep on Turnin".  almost unrecognizable and uncredited to Green.

Strange Variation 2 -  "Battleship Chains" Georgia Satellites (Terry Anderson) covering The Woods (Terry Anderson's first band) and later covered by Hindu Love Gods (basically, REM plus Warren Zevon.)

Special Mention: Kid Creole's irresistibly danceable yet hilarious cover version of Harry Belafonte's "If You Wanna Be Happy For the Rest of Your Life (Never Make a Pretty Woman Your Wife).

Jimi Hendrix - Hey Joe

Another song w innumerable covers:
Martin Gaye's "People Get Ready" 
My favorite cover is the acapella version by The Persuasions.  Another great cover by Eva Cassidy. 

The first song mentioned by the OP, "Baby Blue," is actually two different songs with the same title.  The Badfinger song is the not Dylan song.  FWIW I love the 13th Floor Elevators' cover of the Dylan tune on their "Easter Everywhere" LP.

Here are a couple of covers that I really enjoy. Both are on the same album too.....

From Brain Auger's Oblivion Express album - "Compared to What" and "Inner City Blues".

"Compared to What" is a Les McCann song, first recorded by McCann and later by Roberta Flack. The Brian Auger version takes the original jazz version into Jazz/Rock fusion territory.

Of course "Inner City Blues" is a Marvin Gaye song off of the incredible album "What's Going On". Auger takes the original R&B tune again in to Jazz/Rock fusion territory.

I've had the Brain Auger record since sometime in the '70s and I still enjoy it regularly.