Yay Rohan! I usually play all-mounted Rohan armies because I find them very fun and maneuverable.
Riders of Rohan, though they have the bow issue as whafrog mentioned, are your cheapest mounted units. They are good for bolstering your lower cav numbers and to get bows in.
I haven't used Rohan Royal Guard very much because I tend to play against Isenguard and dwarves the most (F4, good defense, lots of S4). The F4 is helpful, but seeing as the D6 is useless against S4 units and I'm not facing many terrifying units, the RRG are usually not worth it for me. If you are playing against more "normal" armies with lower fight value and strength 3, then they would be very useful for their survivability and increased chance of winning the fight.
Sons of Eorl are my personal favorite Rohan unit. They are one of the only things that is truly and awesomely unique to Rohan (other factions can get throwing weapons, various cavalry with lances, cheap heroes, etc.). Several other factions can get nice shock troops (Iron Guard, Beserkers) with 2 attacks, but Rohan is the only one with a 2-attack cavalry warrior. Granted, they are quite expensive and they don't have lances like Knights of Dol Amroth, but they do still have armored horses and D6, plus S4 and 12" movement. The double attacks turns into 3 on the charge and 6 strikes if you win the fight. And, at S4, this is the same attack potential as most of the medium-level double attack/wound Rohan heroes. Since I fight against D6 units a lot, the S4 really helps, though against Uruks, taking wounds on a 5 is not so nice. The awesome thing about these guys is a nice, small squadron has quite a bit of hitting power, enough dice to take on multiple enemies alone, and a not-so-bad chance of surviving even if they don't get the charge (just in case...). The two attacks when counter-charged lets them win the fight on equal terms with a KoDA (with Dol Amroth for Gondor! rule), but they also get 2 attacks at S4 rather than 1A at S3 (no lances without the charge).
The 12" movement helps for flanking maneuvers or getting to objectives before the enemy. Eorl the Young also has a 12" movement also, though he limits allying options. A small group led by him with another normal cav group led by a King of Man would work pretty well. One of my favorite things to do is have Gandalf on Shadowfax with two Sons of Eorl as his "thugs" or bodyguards. The whole little trio can move at 12", and if there is a problem, the Sons of Eorl can deal with it while Gandalf casts spells. A great little death-squad.
If not with Gandalf's blinding light, I would shield the Sons of Eorl behind RoR as you approach the enemy, to protect them from bowfire. 22 points to be shot down on a 6 is a bummer.
So yes, obviously I like SoE a little bit
. They really help give Rohan a more strong front against elite armies, and easier trampling power against normal warriors. Just don't get too many, as they suck up points very quickly. Anywhere from 2-6 in a 700pts game is good. And remember, its 22 points for a warrior that is on par stat-wise with most of the lower-class Rohan heroes (without MWF of course) AND with a 12" armored steed to boot.
Outriders on horse are a pretty good deal, though the D4 makes them vulnerable to S2 arrows and D4 enemies. Gandalf's Cast Blinding Light can help give you the archery advantage though, especially as outriders are immune to bow limit. Be careful though-- since they are all heroes technically, they have to test individually for their courage tests. Taking a horn in outrider-heavy armies is a good idea. Other options are Saruman the White's 12" hero-inclusive stand fast, or Halbarad's 6" banner-of-no-fear (automatic passed courage tests if in range).
For the throwing spears, I've found that they are more effective on infantry against low-defense armies. In the infantry, you move around a lot more in the 6" range than on cav (staying out of charge range). They can be good to force someone out of a turtle. If the enemy is holed up between terrain with a full pike block, they have the option of staying and taking the TS hits or being forced to leave their position to engage your units. A good balance of throwing spears on the cavalry can help too, but they do suck up points if it is overdone, especially in smaller, all-cav armies.
Hope this helps a bit; sorry for the long rage about Sons of Eorl.