A list of the first ascents of non-eliminate problems at each grade. Traverses are in a seperate list below.
Some problems were originally the starts to routes, but the nature of bouldering has evolved over the years and this list represents the progression of climbing standards on what we currently call boulder problems.
5 - Victorian Climb - Simon's Seat - ? - 1895
6A - Flipper - Robin Hood's Stride - ? - 1903 photo (Flipper is the climb on the right, without the cheat stone)
6A - Spider Wall - Ilkley - ? - 1930's? video
6A - Crease Direct - Crookrise - Allen Austin - 1957 (beats Crucifix Arete by a year and The Villain by two)
6A+ - Teaspoon Variation - Almscliff - Arthur Dolphin - 1948
6B - Janker's Groove Direct - Froggatt - Don Whillans - 1948?
6B+ - ?
6C - Syretts roof - Almscliff - John Syrett - early 1972 (beats Horror Arete by two years) video
6C+ - Tom's Original - Stoney Middleton - Tom Proctor ? - 1960s? (given 7A, but generally regarded as a bit soft.) video
7A - Barleymow - Almscliff - Tony Barley - 1966 video
7A+ - Ron's Crack II - Crookrise - Ron Fawcett - 1974 (beats Red Baron and Desert Island Arete by two years) photo
7B? - Jerry's Arete - Bridestones - Jerry Peel - 1970s? (grade reflects original state - it used to have better footholds) photo
7B - Bald Pate Superdirect - Ilkley - Andy Brown - 1980
7B+ - Lay-By Arete - Slipstones - Paul Ingham - 1983 (beats West Side Story by two years) video
7C - Cental Wall Direct - Dib Scar - Rob Gawthorpe - 1982 (the start to a route, not generally considered a boulder problem, though it is probably possible as such.)
7C+ - Haston Problem - The Breck - Stevie Haston - 1979
8A - Careless Torque - Stanage - Ron Fawcett - 1987 video
8A+ - Superman - Crag X - Jerry Moffatt - 1988 (a tight line. holds have altered.) video
8B - Isla de Encanta - Trowbarrow - John Gaskins - 1999 video
8B+ - Kaizen - Woodwell - John Gaskins - 2001 photo
8C - Walk Away ss - Fairysteps - John Gaskins - 2002 photo
6A - Three Swings Traverse - Almscliff - ? - 1940s?
6B - Traverse - Shipley Glen - ? - 1950s?
6B+ - Virgin Traverse - Almscliff - ? - 1970s?
6C - Demon Wall Roof Traverse - Almscliff - ? - 1970s?
7A - Bluebell Wall Traverse - The Breck - Al Rouse - 1968
7A+ - Pebble Mill Traverse - Burbage South - Pete Lowe - 1978 video
7B - Pebble Traverse - Stanage - Ron Fawcett - 70s/80s?
7B+ - Mid-level Traverse - The Breck - Mike Collins - 1979
7C - Powerband - Raven Tor - Jerry Moffatt - 1987 video
7C+ - Pockets traverse - Back Bowden Doors - Pete Curtain - mid 80's
8A - Staminaband - Raven Tor - Ben Moon - 1988 video
8A - Traverse of the Gods - Craig Y Longrdige - Tony Mitchell/Dave Kenyon - late 1980s? video
8A+ - Inertia Reel Traverse - Jerry Moffatt - Roaches - 1980s? video
8B - Anesthesia - Woodwell - John Gaskins - 2000 (originally graded 8B/8B+, but climbed with an eliminate no heels sequence) video
8B+ - Pilgrimmage - Parisella's - Malcolm Smith - 2004 video
8C - History awaits...
UKB thread 
UKB thread