However, thats not to say some civs don't fit some play styles better.  If you enjoy early war and conquest, the Romans or Persians might be better for you based simply on their UU.  Maybe you enjoy being the culture giant...  In which case the babylonians might be better for you. 

I find the traits are more useful then the unique units though.   I know I've pasted this in another thread, but I can put it up again:

Traits (copy and paste time ) Lets put them in categories as to their benifits: Early Game: Expansionist Militaristic Late Game: Scientific Commercial Any: Industrious Religious Expansionist: Early game this is a huge advantage... The early scouts can uncover great bonuses in them goody huts... Use this trait well early (make 3 or 4 scouts and get those goody huts)... By the middle ages it becomes a useless trait. I notice expansionist AI's do better early, but fall behind later. Militaristic: The cheaper barracks make a difference early on when you're making 2 or 3 shields per turn, but the fact it's only 20 shields cheaper isn't as good later on in the game. The elite units will come quicker as well... Early on it's a great help as your military isn't all too large. Late game when you have 200 units under your command, the couple extra elites are no biggie. Scientific: Huge bonus's from scientific, if you can live to see them. The first benefit isn't until literature (making it the latest 'first benefit' of the traits)... So if you can survive and thrive till then, great. In my opinion, the 3 free techs + cheaper library/university/research lab makes this trait stand out as having the biggest bonus's, but the fact that it doesn't kick in til later game makes it less attractive Commericial You don't see much bonus from this until your empire has gained alot of size. If you are playing towards owning a huge empire, this trait is amazing (the effect on corruption can't be understated) and the bonus trade to cities is a decent bonus too. Great bonus', but the waiting til later game makes it less attractive. Should note, this trait is the only one skill level dependant as well. Lower difficulties with less corruption won't notice as big of affects as someone on diety will Religious: Kicks in right away with cheaper temples (30 shields cheaper, which is a huge bonus) and continues helping out when you reach cathedrals. The Anarchy time reduction is invaluable Industrious: Starts helping with the very first turn and building that first road and continues to ensure that you're land is well developed. Bonus production to cities will help later in the game as well. Agriculture and Seafaring for those playing C3C: Aggy can have the biggest affect in the game. An additional food from the start (assuming you started on a river) will allow you to make settler factories without the need for a bonus resource tile. Cannot state the helpfulness of this... A regular civ on a river will have it's city increase in size at the rate of 10 turns per increase (assuming you keep building settlers and workers keeping the size down). In 60 turns thats 6 extra population (or 3 settlers worth). For the aggy civ, thats 7 turns per increase, or 42 turns for 6 population... The rate you grow at is phenomenal. In addition to the extra food on the home tile, the ability to use desert tiles as if they were plains is anothr huge bonus... You aren't limited by one of the most limiting tiles (deserts) and you can thrive in conditions that other civs can't (It's like adding a space trait and allowing the space civs to build on the moon that only they can access). Very unbalanced trait giving by far the best bonuses... Though it can be map limited. A small archapegelo isn't going to have many deserts or rivers for you to take advantage of. Seafaring +1 trade per ctiy on the coast line is a nice bonus... You are the only civ that can get 5 trade per turn from a size 1 city (atleast off the start) and this bonus can really give you a tech/gold catapult off the start. It's downfall is the dependancy on the map type... It's a huge advatage on water maps, but is pretty useless on a large pangiea. The sea movement for ships and lower chances of sinking allow you to map out the globe early on and gain contact with civ's thats nearly impossible for others to have (if you're continental, the advatages you can gain by getting a curragh to the other continent and trade with those nations (that the nations on your continent don't have contact with) will allow you to manipulate tech trade really well. I find that all traits have their advantages and each really is no less than others. It's the combinations that make the differnce. For example, sea faring expansionist = silly combo. Trait best with islands combined with trait best for pangiea? Combinations I like as they compliment each other: Industrious / Religious Commerical / Industrious Religious / seafaring (ocean maps are hard to get high productions on.. the cheap temples is amazingly helpful) sear faring / scientific (same reasoning as above) Militaristic / commercial (expand you empire through early war and keep it less corrupt) Expansionist/scientific (earliest helpful trait combined with latest game trait) Aggy / industrious (populate the land as quick as possible and provide the infrastructure to keep the high population producing it's best) Aggy / Religious (Can whip so many of those extra population units into temples that nobody can keep up to your culture) Commercial / Seafaring (large overseas empire) Commercial / scientific (Survived the early game and you're traits will stand out to no end) Religious / scientific (ultimate in culture) There more good combinations of course, those are just my preffered.

Scandinavia...  You are correct, they aren't the best trait setup.  If you look on the art of war section you'll see a save game from a scandinavia game of mine that I tried to put together a viking republic.  The unique nature of the Bezerk made for an extremely fun game.

Aztec, America, Mongols, Portugal are my no plays for the most case as their traits or UU just seem silly.

eddit:

http://www.1bcciv.com/Topic2205858-16-1.aspx for the scandinavian game

1. make contact with everyone quickly

2. be crafty about trading and stuff to get ahead of everyone in techs and gold early, and leave them in the dust.

3. Crank out the towns!!!!!!!!!!!

4. Do not go for a solid infrastructure, two buildings per city is max until about midway or later through Middle Ages, expand, conquer, expand, conquer, expand, conquer . . .

5. have a good intuition for the level of development all your opponents at any particular time, and  start planning to hit them where they are weak early.

4. Build a ton of those fast warrior guys, but put off using them until the last possible moment.

My personal fave to play are the Babylonians, just because...

cos they are scientific so you can keep up with the science race plus their comercial helping so much against corruption als othe sturdy hoplites help keep you safe in the early game periods