Artillery is scary for Eldar.
Fortunately though we have the tools to deal with this. As has already been stated, Void Spinners are your friend. Not only that but long range vehicles like Fire prisms and Scorpions do the business too.
Since it's only really Guard that can hit you with artillery in the opening phases of the game, chances are very high that you'll go fist and can shut down his arty with your VS counter-battery fire.
Warhounds are another one that can be worrying. Usually though if you're playing against marines they'll have very little to deploy (Or less than you do anyway) meaning that the warhounds are placed before you put down your mounted infantry fms. Just pre-measure their threat range and make sure you're out of it to prevent the Alpha strike.
Another thing that I quite often like to do against Warhounds is to set up my troops in such a way that if they do choose to Alpha strike my mounted infantry then they are severly punished for it. 2 crossfiring falcon fms make a very quick end to a Warhound and that's all to the good. I'll take the damage to my MI if it means I can kill the warhounds off nice and early.
Spaceships are pretty decent too, if you can get the hang of reading the terrain. I have aquired the knack of being able to read the terrain and guess 8 times out of 10 where my opponent is going to place his arty and orbital bombard the snot out of it. They're also very nice for pinpointing shieldless warhounds. I have an enduring loathing for warhounds and take great pleasure in ending the little feckers from Orbit.

My Eldar lists always include lots of mounted infantry, as they are simply superb once you get the hang of them.
Lists below are EUK:
Biel Tann:
The Stompwind!, 3000 POINTS
Biel-Tan Craftworld (Epic-UK v20101230)
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AVATAR [0]
ASPECT WARRIOR WARHOST [600]
4 Dire Avenger, Exarch, Autarch, 4 Wave Serpent, 2 Striking Scorpion, 2 Fire Dragon
ASPECT WARRIOR WARHOST [350]
2 Exarch, 8 Warp Spider
GUARDIAN WARHOST (MOUNTED) [350]
Farseer, 4 Wave Serpents, 7 Guardians
FALCON TROUPE [275]
3 Falcon, Spirit Stones, 2 Fire Storm
FALCON TROUPE [275]
3 Falcon, Spirit Stones, 2 Fire Storm
FIRE PRISM TROUPE [250]
3 Fire Prisms
ENGINES OF VAUL TROUPE [250]
Void Spinner
ENGINES OF VAUL TROUPE [250]
Void Spinner
RANGER TROUPE [100]
4 Ranger
RANGER TROUPE [100]
4 Ranger
VAMPIRE RAIDER [200]
http://traitor-legion.appspot.com/choos ... 0~11x4~522At 4000pts I like to throw in a Warlock titan to really ramp up the rolling assaults and give my opponent headaches.
At club level, I'm rarely beaten when using this list. It's only when attending tournaments with the big boys that I have my lunch money taken and even then I don't make it easy for them (Well, too easy anyway).
Ulthwe:
Stomp'thwe, 3000 POINTS
Ulthwé Craftworld (Epic-UK v20101230)
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AVATAR [0]
BLACK GUARDIAN WARHOST (MOUNTED) [475]
4 Waveserpents, Farseers, 6 Guardians, Seer Council
BLACK GUARDIAN WARHOST (MOUNTED) [375]
4 Waveserpents, 2 Farseers, 6 Guardians
BLACK GUARDIAN WARHOST [225]
2 Farseers, 3 Guardians, 3 Support Weapon Platforms, 3 Heavy Weapon Platform
FALCON TROUPE [275]
3 Falcon, Spirit Stones, 2 Fire Storm
FALCON TROUPE [275]
3 Falcon, 2 Fire Storm, Spirit Stones
FIRE PRISM TROUPE [250]
3 Fire Prisms
ASPECT TROUPE [275]
Exarch, 6 Warp Spider
VAMPIRE RAIDER [200]
NIGHTWINGS [300]
3 Nightwing Interceptors
WRAITHSHIP [150]
RANGER TROUPE [100]
4 Ranger
RANGER TROUPE [100]
4 Ranger
http://traitor-legion.appspot.com/choos ... 4~500~11x44000 pts sees the addition of 2 x Scorpions and some more mounted Guardians (Because they are that good).