Springing off a comment on my last post, here are some thoughts about the non-combat abilities some DF templates bring to the table. These are my experiences, and may vary from yours.
The knight brings a single-minded dedication to combat to the table in DF. So much so that unless you deliberately diversify into some kind of non-combat ability, you don't have any significant ones.
You do still have some utility, even so. Most knights seem to opt for fairly hefty armor, and come with solid ST and DX right out of the gate even without enhancements from your optional trait pool. Don't overlook these - you'll be good at carrying gear, loot, fallen comrades, etc. You can handle DX-based tasks reasonably well. While your focus is almost purely combat, a few points in skills like Stealth, Climbing, Swimming, Carousing, etc. can round you out well.
Adding in Forced Entry makes you a good door forcer - less so than a barbarian (unless you up your ST and the Forced Entry skill) but you'll be properly placed for any fight that occurs. I highly recommend taking Forced Entry. The bonus to destroy non-animate things is handy, too.
Basically, though, you're a mobile engine of destruction, and your non-combat abilities spring from the basic scores that feed your core aspect.
Barbarians are excellent combatants, although they're not top-tier like the almost exclusively combat-focused knight and swashbuckler. They have way more non-combat abilities than either of those, though.
To some extent, the non-combat abilities you bring to the depend depend on what kind of barbarian you are. A savage warrior, a survivor, and a rage barbarian all bring different things to the table than a standard barbarian. But they vary more in degree than kind, overall.
Outdoors skills are the main area where barbarians shine outside of combat. You've traded a lot of combat utility for outdoor skills, Survival, Tracking, etc.
Your ST is the highest starting of any of the characters, but it's trivial for knights to keep up for a while (although you max higher, given the same race.) You've got a lot of HP, too, so you make a good door-opener, trapped-chest basher, and overall damage absorber. You are good at surviving, and if it's seems likely HP must be spent to accomplish a task, you're the one to do it. Like the Knight, your ST and DX make you viable in any physical task, and potentially much more so for ST than anyone else.
Consider the barbarian - especially the standard one - as the best outdoor type who trades back some non-combat utility in the dungeon or in urban situations. You will be hard to live without outdoors, and mostly useful for ST and combat indoors. But don't forget Tracking, Stealth, and your respectable Per for keeping an eye out for things. If you're lightly armored, you'll be fast, too, opening up a chance for scouting or trailing back in the rear while still being able to close in if needed.
Wizards are a special case. You can't add as much to combat as the dedicated fighters, not without basically crippling their great strength - diverse spell-based abilities. You're more of a niche combatant, in that you have area spells, costly attack spells, and buff spells at your fingertips. You can pull your weight in combat with the right spells, but dedicated fighters can vastly exceed your capacity for damage in the short and long term.
However, you have almost niche-destroying breadth of ability. You can bypass obstacles with Movement spells, substitute for hirelings with Illusion and Creation spells, boost the combat abilities of everyone, make undead help, find traps, negate the abilities of non-magical foes, detect treasure or foes or any other needed substances, divine answers, set fires, dig tunnels, etc. etc. etc. If you take Wild Talent with Retention, you'll be rolling in spells in no time. It's actually harder to be a combat specialist than a broad support wizard who can help everyone do everything and/or partly replace other templates.
You also have a lot of non-magic non-combat abilities. Alchemy, identifying magical goodies, scooping hazardous material for loot, and so on. Plus your high IQ and solid Will means you can easily diversify into a broad array of mental skills if you need them. Diplomacy, Cartography, and other mental skills are on your template and you can make a good substitute speaker and scholar.
The only things I find that stop wizards from rampant niche-stomping are the FP costs of doing everything with magic and points. You never have enough points for all of the spells you think you need, and not half of enough for all the spells you'd like to have handy. Try to remember you're better off doing the non-combat things other don't do instead of trying to match or beat other delvers you adventure with.
It doesn't hurt if the GM is liberal using No Mana Zones, Low Mana Zones, Magic Resistance on foes, magical opponents (critical!), meteoric weapon armed foes to mess with your Blocking spells, and pushes the pace so you can't turn every fight and every obstacle into a blow-all-FP-and-rest routine. You're still the best overall tool a party has for dealing with the world as a while in a non-combat fashion, especially in dungeons.
Next time, I'll tackle a few more professions and what I see are their non-combat utilities. I'll strictly be sticking to ones I've seen in play, so please don't ask about Bards, Sages, and so on - I just don't have an opinion that comes from experience.