Undercover Of The Night - Rolling Stones
Up Around The Bend - Creedence
Under My Wheels - Alice Cooper
Under My Thumb - The Rolling Stones
U.S. Blues - The Grateful Dead
U.M.C. (Upper Middle Class) – Bob Seger
Uncle John’s Band – Grateful Dead
Under African Skies – Paul Simon
Up on Cripple Creek – The Band
Us and Them – Pink Floyd
Both already posted.
Ukulele Lady - Bette Midler
Unbelievable - Diamond Rio
Undecided - Ella Fitzgerald
United We Stand - Brotherhood Of Man
Up A Lazy River - Louis Armstrong
Undercover Angel- Alan O’Day
Unchained Melody- Righteous Brothers.
Up Around the bend- Creedence
Unforgettable- Nat King Cole.
Only four for U
Already nominated. 
Clearly sir, you are a person of taste and refinement.
Yeah, everybody says so!
Unbelievable - EMF
All the other ones I can think of right now have already been named.
The Unheard Music - X
Ugly Boy - Die Antwoord
Up On The Roof - The Drifters
Not nearly as fertile as ‘W’ was.
I mean, there are always half as many Us as double-Us, by definition.
Man, those guys got everywhere.
Nope- Post #5
Beat you to it 
Unchained - Van Halen
Unsatisfied - The Replacements
Up The Neck - The Pretenders
Undertaker - Southern Culture on the Skids
Up the Ladder to the Roof - The Supremes
Un Alma Mas - Josh Groban
Up on the Roof - James Taylor
JT’s cover is the version I like best
Uncle Walter - Ben Folds Five
UHF - Weird Al Yankovic
The Usual Thing - Marshall Crenshaw
The Unattainable Earth - Daniel Amos
The Understudy - China Crisis
I was going to post that, but apparently it’s actually called “(Up A) Lazy River” …
(And i would probably have chosen a different (instrumental) version !)