Disease resistance in roses is a very subjective thing:- Iceberg for instance is a popular healthy rose, as are the Flower Carpets, yet both can mildew quite badly on occasions.
In recent years breeders have paid alot more attention to disease freedom, with increasingly good results. However most rose health information is anecdotal.  Here in Australia many new roses are being screened at the Adelaide National Rose Gardens for disease resistance.   There are a great many roses described as "healthy" but only included here are those with some acclaim to resistance.  Similarly, there are a great many promising varieties which may match or surpass these presently listed.  Naturally, comments are welcome regarding the observed health of any listed (or otherwise).  Unfortunately the terms "healthy" and "resistant" are somewhat interchangeable but "disease free" is quite precise.  Note also that here priority is given to health over floral prowness; but breeders are rapidly converging the two traits.  Perpetual flowering, scented, disease free, thornless roses; here we come!   The list following contains a mixture of bush roses, climbers, miniature and ground covers etc. (Caps are incidental)

Rose  Released Colour Height Perfume Flower type Resistance Details Class

Alberic Barbier White   shade tolerant white
Aotearoa New Zealand -  pink      HT bush
ARCHIDUC JOSEPH  Red Tall *** Double ***** Brick to carmine red, recommended Tea aka Monsieur Tillier  red    *****  tall HT
AUSTRALIA FAIR * Pink Low *** Semi-Double ***** Named to honour our Centenary of Federation Bedding  Pink    *****
BANKSIA DOUBLE WHITE  White V.Tall *** Double ***** Thornless, masses of flowers in spring, sweet scent Species  white    *****
BANKSIA DOUBLE YELLOW  Yellow V.Tall * Double ***** Thornless, masses of flowers in spring Species  yell    *****
Bonica pink  pink   cluster  prolific Bush
Cecile Brunner Climbing Climber; light pink, light fragrance, up to 12ft. Walls and arches   Pink      Climbing
Compassion Large-flowered Climber; pink, shaded apricot, very fragrant (M)   Pink      Climbing
Complicata (Ariana d'Algier)  pink blend    not repeat  Med. Frag. Gallica
Crystal Fairy (PGA) 2002 white .5m  The fairy/ White Carpet type   Ground cover
Dublin Bay (Macdub) Large-flowered Climber; deep red, some fragrance (S)   red      Climbing
EGLANTERIA  Pink Tall *** Single ***** Lovely aromatic foliage, spring Old
Ekstase PBR (Kordes) Highly fragrant cut flower variety. The red blooms are produced singly and also several to a stem. Plant habit is strong with healthy dark foliage. (Standards $25.00ea.)  red
Elina Very large well formed blooms of lemon to light yellow. Freely produced on a plant of exceptionally healthy and plentiful growth.  yell
FLINDERS  Pink Low *** Double ***** Good low shrub/ground cover. Little maintenance Clg/Ramb/GC
Flower Carpet Pink (Noatraum) Ground Cover Shrub; deep pink, some fragrance (W)    Pink      GC
Friesia syn Sunsprite * Yellow Medium ***** Semi-Double *** Intense clear yellow in clusters Bedding
FRU DAGMAR HASTRUP  Pink Low *** Single ***** Continuous display of large blooms Early recurrent
Magic Carpet (Jaclover) (hb) Ground Cover Rose; lavender, fragrant   Lavender
MAWSON * White Low *** Semi-Double ***** Best described as a low growing Iceberg Bush
Mme Plantier  white   not repeat  Med. Frag. Alba
New Dawn Rambler; shell pink, fragrant (M)   Pink Low *** Double *** Repeated display , thick glossy foliage Screen
ONKAPARINGA  Pink Medium ***** Double ***** Australian bred rose of exceptional performance True Blue  Pink    ***** prolific Bush
Our Rosy Carpet Masses of semi-double, rose pink blooms are produced continuously. Extremely healthy and hardy. Approx. 80cm high by 1.2m wide. Also makes an excellent 80cm standard or tall weeping standard. $9.50ea or $75.00 per 10, $300.00 per 50,   Pink
Precious Platinum An excellent dual purpose rose of very good growth and disease resistance. Blooms are bright crimson red produced singly on long strong stems. Dark green foliage. Highly recommended.  red
ROSERAIE DE L'HAY dark red Medium *** Semi-Double ***** Large double peony-like blooms Rugosa  red    *****  Modern Rugosa
Rugosa Roses - all varieties
RUGSPIN  Lavender Medium ***** Single ***** Very large blooms and hips Early recurrent Rugosa
St. Patrick - yellow blend   yell      HT
Star Struck PBR Multi-petalled blooms of pastel peach to buff apricot are produced continuously in large clusters. A tough landscaping or hedging plant with excellent disease resistance. Ideal as a specimen or planted en masse. Winner of the 1999 Hardiest  apricot 1.5x1.2    contin bush
The Mayflower 2003 Pink Bush   completely res. David Austin Heritage
Traviata (Meilland) 2002 red bush med 1.2m  old fashioned   heritage
 

References
Botanicas Roses Random House 1998 Peter Beales et al.
The NZ Book of Roses John Martin & Colin Hutchinson 1992 Palmers Gardenworld & Whitcoulls
With special acknowledgement & thanks to:-

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