Roth IRA vs 401(k) (or 403(b))
For this post, 401(k) means traditional, not Roth 401(k)s which are brand new and generally not available.
Reasons why one would want a Roth over a 401(k)
1. They are in a lower tax bracket then they will be at retirement.
2. You can invest in anything you want, not a company (school) sponsored 401(k) or 403(b).
3. The company 401(k) may have high fees or poor performaning plans. Although the company may be able to get you a better deal. This probably unlikely if you are just going to invest in index funds anyway.
4. You do not have to make withdrawals when you hit 65 like a traditional IRA (and 401(k), although I'm not sure about 401(k)). If you are well off and do not need the money right away this could be important.
5. The contributions to a Roth IRA can be taken out without penalty (but not the gains)...although you shouldn't do this it is nice to know it is there.
6. The money in your Roth can be taken out be used to buy a house (although you probably shouldn't do this.
Reasons why one would want a 401(k) over a Roth
1. There is a company match that is dependent on employee contributions.
2. The company may be able to negotiate a lower fee than you could get on your own.
In a perfect world you would probably want to have both.