Doing Things That Aren't So Hostile
In addition to combat abilities, characters have access to skills, which let them do things ranging from leaping over things to talking the merchants into giving them better deals.
Each class has a list of skills that they are proficient in, everything else is considered "cross class" and is harder for them to learn. You'll get a certain number of skill points at each level, based off class, with bonus points for having a high intelligence or being human. At first level you get 4 times the skill points. Skills are allowed up to a maximum of your total level+3, and half that for a cross-class skill (so a level 12 character could have his skills up to 15, or 7.5 for cross class). Regular skills cost you one skill point to raise one rank, cross class will raise a half rank for one skill point. If you have a multiclassed character, you can raise skills up to maximum, but the class you take each level in decides how much you get for your skill points.
Example: Bob the Fighter 3/Ranger 3 decides he wants to be able to see things coming for him, and buy some ranks in spot. When he reaches level 7, he takes a level of fighter. He can raise his spot skill to 10 (level 7+3), but he's going to have to pay a skill point per half rank in it, since spot is cross-class for fighters. If he took ranger instead, he'd still have a maximum value of 10, but he could buy it at a rate of one rank per skill point, since spot is a class skill for rangers.
DDOWiki has a good summary of skills
Balance - get back up quickly
Bluff - allows you to sneak attack something that is angry at you. Rarely bought due to a long animation time.
Concentration - keeps you from getting distracted when casting in combat
Diplomacy - talks things out of hitting you and into hitting your friends
Disable Device - shut down a trap
Haggle - get better prices when buying/selling
Heal - allows everyone but warforged to get more HP at a shrine
Hide - exactly what it sounds like
Intimidate - makes things attack you
Jump - Boingy! Boingy! Boingy!
Listen - allows you to hear stealthed enemies when they move
Move Silently - keeps enemies from hearing you when you're stealthed
Open Lock - gets you into places you should not be
Perform - for Bards, determines the DCs on their fascinate ability and which songs they can learn
Repair - allows warforged to get more HP at a shrine
Search - find secret doors and traps
Spot - see enemies that re trying to hide you, get warning traps and secret doors are around
Swim - swim faster and hold your breath longer
Tumble - take less damage from falling, and roll around like a cannonball (backflips if you get high enough)
Use Magic Device - use magical items you wouldn't otherwise be able to use, such as wand or race-restricted weapons
Wait, You Want To Do What?
Staying on your feet
The balance feat is highly recommended for front line combat types. Its claim to fame is that balance governs how fast you get up after you get tripped, which happens pretty often whenever there are dogs or wolves around.
TO engage in stealth effectively, you need both of the stealth skills and some way to see anything that's trying to do the same to you. The standards are:
You need both hide and move silently, as critters can both see and hear you. Spot lets you see where any stealthed sentries are, so you don't bump into them and find yourself surrounded by things that don't like surprise visits.
For some really good information, see Part IV of SableShadow's Rogue Guide
Play with the enemies minds:
Intimidate and Diplomacy - these let you move enemies around.
Intimidate is a pull, getting things to come straight for you. You need some way to handle it - high AC, damage reduction, or some sort of nastiness to drag them through.
Diplomacy is a push, getting things to stop chasing you and move to the next most hated person on their list. It's not a guaranteed 6 seconds of joy on your part, since if you injure them, they'll be more than happy to go back to chewing on you.
Bluff lets you convince something to turn around so you can stab it in the back. Unless you take the Improved Feint feat, this is a long animation when you use it. Most people don't invest in this skill for that reason, but some like the fact that it gives them a few seconds of confusion when things aren't hitting them.
Remove all those nasty traps:
Spot, Search, and Disable Device. Spot gives you an alert that there is a trap nearby, search lets you find the trap, and disable device lets you shut it down once you find the box. Be sure to keep your equipment up to date when doing this - if you fail a trap roll by 5 or more, the trap box blows up and you can't try again. Veteran players often have trap locations memorized, and don't take the spot skill.
Sableshadow comes through again with a compendium entry about trapsmithing.
Bounce over things' heads and get into interesting places:
The jump skill is great for mobility, allowing you to simply go over things you can't get around. It has a hard cap of 40 - this was put in so that dungeon designers knew the upper limits of people's reach. Monks have an ability called Abundant Step, mimicked by Favored Souls' Leap of Faith, both of which allow you to get a short boost in speed through a jump. These are awesome for people who want that extra edge while exploring Stormreach.
Casting in battle or amassing large amounts of ki:
This is the Concnetration skill. Spellcasters need it to avoid losing a spell when damaged during casting. The higher your concentration, the more damage you need to take at once to get interrupted. Monks use the concentration skill to determine how much ki they can hold onto. Your concentration skill determines how large your stable ki pool is, and how fast it dissipates when you have more than that.