The Lost Single

Great singles that were not on albums are a thing of the past. Only the great show-offs could really do it. You could include B-Sides too - in that case Oasis were the last band able to do it. But in terms of great A-Sides that were not on albums you'd probably have to go back to The Jam for the most recent group. Nowadays, the purpose of a single is to promote an album. Back in the old days you were expected to produce new product every few months. Anyway on to the (preliminary) list:

Bob Dylan - Things Have Changed
Bob Dylan - Positively 4th Street
Bob Dylan - Can you please crawl out your window? (B-side)
The Jam - Going Underground
The Jam - Butterfly Collector (B-Side)
Oasis - Masterplan (B-Side)
Beatles - She Loves You
Beatles - I Want to Hold Your Hand
Beatles - This Boy (B-Side)
Beatles - Hey Jude
Beatles - Dont Let Me Down (B-Side)
Beatles - Rain (B-Side)
Beatles - Strawberry Fields
Beatles - Penny Lane
Beatles - Daytripper
Beatles - We Can Work It Out
Beatles - Ballad Of John & Yoko
The Who - Substitute
The Who - Pictures of Lily
The Who - Anyway, Anyhow, Anywhere
The Who - Can't Explain
The Who - I'm A Boy
The Who - Happy Jack
The Who - The Seeker
The Who - Magic Bus
Rolling Stones - Jumping Jack Flash
Rolling Stones - 19th Nervous Breakdown
Rolling Stones - Have You Seen Your Mother, Baby, Standing in the Shadow?
The Kinks - Dead End Street
The Kinks - Berkeley Mews (B-Side)
The Kinks - See My Friends
The Kinks - Days
The Kinks - Autumn Almanac
The Kinks - Wonderboy
The Kinks - Polly (B-Side)
The Clash - (White Man) In Hammersmith Palais (released on belated US album)

Of course, its all a matter of taste. you could easily pick 5 or 6 more from the beatles, for example. These are just songs I can think of at the moment. There are probably plenty more. As can be seen from this list, the single was the most important thing in the pre-Sgt Pepper era and then that album kind of changed things. As Paul Weller said recently "You'd never get away with that now"