Soloing Is doable and here are some examples of quests that friends of mine have run. They are more difficult but doable and after you max out a character you can get bored.
As a level 5 rogue you can solo Shan-To-Kor.
It's really not that hard, use alot of ranged weapons, sneak past things you don't have to kill.
Only real problems are:
earth elementals (I used magic missle wand w/ UMD on those).
Locked room at the end of that same part with the earth elements... I jumped up onto the throne... grabbed the wall above it... pulled myself up... and played "dodge the searing light" with the cleric for a bit, ended up shooting everything till they died =P
Giant at the end took forever (thank god for adamantine returning throwing axe).
Soloed Shan to korr part 1 2 3 as a lvl 2 ranger/2 fighter, you just need to be careful and have shot on the run. Shan to korr and redwillow and catacombs part 1 2 3 is as far as I could solo.
My favorite solo experience was Redwillow with my level 6 dwarf cleric. It was more-or-less a breeze, and the giants were lots of fun. I felt like I was truly roleplaying my dwarf by twitch-dodging stomps in addition to my built-in defense. I had 3 on me at one point, but still managed to avoid getting hit. In fact, I only took 5 damage from that entire giant camp, and it was from a hobgoblin. The gargoyles were probably the closest encounter to killing me in the quest, as I accidentally pulled the granite and the named one at the same time. The dark elves went down pretty fast with the aid of a summoned hell-hound to keep everyone but the leader occupied while I dispatched him.
Other interesting solos were Delera's Tomb part 3 (Delera did kill me once), Fire Caves on hard @ level 5, Irestone Inlet @ level 4 (I got really good at strafe-dodging rays), Shan-to-Kor on hard, and Splinterskull on hard (this was absolute cake). Waterworks was successfully completed at level 2, although I skipped all of the ogres the first time around; I killed them all when I came back at level 3.
I think I've soloed all of the harbor and market quests, most of them at equal levels. Stealthy Repossession was definitely the most unorthodox: I did this at level 3, and simply ran through the quest, striking down every non-prophet in my path while building up a trail of prophets beating on my back. I had to run them around in circles until they were far enough off of me to give me time to pull levers uninterrupted.
The key to my success is equipment and spell selection. Everything I own was purchased at the pawn shops with this character: +1 holy heavy mace, +2 shock sickle, +4 full plate and heavy shield. I have 20 str buffed with Bull's Strength, so my combat stats get obscenely high with proper buffs. Wielding the mace and buffed with BS, Bless, and DF, my attack bonus is +14 and I do 12-29 damage against evil critters. Fire Pro allows me to do quests like Fire Caves and Clean the Air (although the latter is still a major pain in the rear). Also, I have a suit of padded armor of detect secret doors in order to search for doors (after spotting them using my high wisdom + spot goggles). The only thing I wish I had was lockpicking... maybe next time I'll start with a level of rogue, although that would push my power level back by one.
These Exerps were takin from various posts on the official DDO forums and edited and compiled