Astrometry, orbital elements, and ephemerides are available for the following objects. Note that the astrometry is usually not complete! What appears for inner satellites came almost entirely from USNO (FASTT) data, and from Table Mountain (JPL) data. The data for irregular satellites was mostly gleaned from Minor Planet Center data. Data for artificial satellites is from assorted sources, amateur and professional.
Jovian satellites: Jupiter I = Io Jupiter II = Europa Jupiter III = Ganymede Jupiter IV = Callisto Jupiter VI = Himalia Jupiter VII = Elara Jupiter VIII = Pasiphae Jupiter IX = Sinope Jupiter X = Lysithea Jupiter XI = Carme Jupiter XII = Ananke Jupiter XIII = Leda Jupiter XVII = S/1999 J 1 = Callirrhoe Jupiter XVIII = S/2000 J 1 = S/1975 J 1 = Themisto Jupiter XIX = S/2000 J 8 = Magaclite Jupiter XX = S/2000 J 9 = Taygete Jupiter XXI = S/2000 J 10 = Chaldene Jupiter XXII = S/2000 J 5 = Harpalyke Jupiter XXIII = S/2000 J 2 = Kalyke Jupiter XXIV = S/2000 J 3 = Iocaste Jupiter XXV = S/2000 J 4 = Erinome Jupiter XXVI = S/2000 J 6 = Isonoe Jupiter XXVII = S/2000 J 7 = Praxidike Jupiter XXVIII = S/2001 J 1 = Autonoe Jupiter XXIX = S/2001 J 2 = Thyone Jupiter XXX = S/2001 J 3 = Hermippe Jupiter XXXI = S/2001 J 11 = Aitne Jupiter XXXII = S/2001 J 4 = Eurydome Jupiter XXXIII = S/2001 J 7 = Euanthe Jupiter XXXIV = S/2001 J 10 = Euporie Jupiter XXXV = S/2001 J 9 = Orthosie Jupiter XXXVI = S/2001 J 5 = Sponde Jupiter XXXVII = S/2001 J 8 = Kale Jupiter XXXVIII = S/2001 J 6 = Pasithae S/2000 J 11 Jupiter XLIII = S/2002 J 1 = Arche Jupiter XLVII = S/2003 J 1 = Eukelade S/2003 J 2 S/2003 J 3 S/2003 J 4 S/2003 J 5 Jupiter XLV = S/2003 J 6 = Helike Jupiter XLI = S/2003 J 7 = Aoede Jupiter XXXIX = S/2003 J 8 = Hegemone S/2003 J 9 S/2003 J 10 Jupiter XLIV = S/2003 J 11 = Kallichore S/2003 J 12 Jupiter XLVIII = S/2003 J 13 = Cyllene S/2003 J 14 S/2003 J 15 S/2003 J 16 S/2003 J 17 S/2003 J 18 S/2003 J 19 Jupiter XLVI = S/2003 J 20 = Carpo Jupiter XL = S/2003 J 21 = Mneme Jupiter XLII = S/2003 J 22 = Thelxinoe S/2003 J 23 Saturnian satellites: Saturn V = Rhea Saturn VI = Titan Saturn VII = Hyperion Saturn VIII = Japetus Saturn IX = Phoebe Saturn XIX = Ymir = S/2000 S 1 Saturn XX = Paaliaq = S/2000 S 2 Saturn XXI = Tarvos = S/2000 S 4 Saturn XXII = Ijiraq = S/2000 S 6 Saturn XXIII = Suttungr = S/2000 S 12 Saturn XXIV = Kiviuq = S/2000 S 5 Saturn XXV = Mundilfari = S/2000 S 9 Saturn XXVI = Albiorix = S/2000 S 11 Saturn XXVII = Skathi = S/2000 S 8 Saturn XXVIII = Erriapo = S/2000 S 10 Saturn XXIX = Siarnaq = S/2000 S 3 Saturn XXX = Thrymr = S/2000 S 7 Saturn XXXI = Narvi = S/2003 S 1 Uranian satellites: Uranus III = Umbriel Uranus IV = Oberon Uranus XVI = Caliban = S/1997 U 1 Uranus XVII = Sycorax = S/1997 U 2 Uranus XVIII = Prospero = S/1999 U 3 Uranus XIX = Setebos = S/1999 U 1 Uranus XX = Stephano = S/1999 U 2 Uranus XXI = Trinculo = S/2001 U 1 S/2001 U 2 S/2001 U 3 S/2003 U 3 Neptunian satellites: Neptune I = Triton Neptune II = Nereid S/2002 N 1 S/2002 N 2 S/2002 N 3 S/2002 N 4 S/2003 N 1 Planets: Uranus Neptune Pluto Artificial satellites:
You can get ephemerides for most of these objects from the Minor Planet Center's Distant Artificial Satellites Observation page, or from the Jet Propulsion Laboratory's Horizons system, customized for your observing location and desired time span.
Also, Peter Birtwhistle has posted a few more pseudo-MPECs for artificial satellites here.
NExT EPOXI THEMIS-B THEMIS-C STEREO-B STEREO booster = 2006-047A 2000-041B = NORAD 26411 = Cluster II / FM6 Salsa 5O55D41 = probable Cluster satellite; dunno which one 6R10DB9 = unknown, probable rock 6Q0B44E = unknown, P=80d, e=.24, i=41 5X2744B = unknown, P=1.20d, e=.72 5X5E564 = unknown, P=2.64d, e=.46 EJA002 (P=1.01d, i=21, e=.11) 1965-058A 6H61SAT (p=1354 minutes, e=.61) 1983-020A (ASTRON) (NORAD 13901) 1983-020D (ASTRON booster) (NORAD 20413) 2003-061B = NORAD 28141 Cassini Chandra Deep Impact GENESIS Geotail = 1992-044A = NORAD 22049 GS428A (unidentified Molniya) IMP-8 (International desig 1973-078A, NORAD 06893) HJ0110 = unknown, P=1.27d, e=.86 HJ0111 = unknown, P=10d, e=.5 (very roughly) Integral 1995-062B = ISO Rk = NORAD 23716 GS61LA (P=630m, i=26, e=.72; P. Birtwhistle find) J002E3 MESSENGER MRO = Mars Reconnaissance Orbiter Rosetta Vela booster = 1969-046F = NORAD 03956 Unknown satellite (5G4FAAB) (P=1300m, e=.30) XMM-Newton = 1999-066A = 25989U V00278 (P=1.27d, i=7, e=.61) WMAP