To many, engagement rings and diamonds are synonymous, but this isn't the only opinion. For a variety of reasons, some people seek a different stone. I am a firm believer that no option is better than the other. The most important thing is going with what you and your partner prefer.
It is true that diamonds are traditional, and this is meaningful for many people. If the tradition of a diamond is significant for you, then go with your heart. Hey, marriage is also pretty traditional right? The link between diamonds and engagement did start with an epic 1930s ad campaign from DeBeers; merely an interesting fact to some, others feel diamonds are less about romance and more about marketing.
It is also true that they are the hardest available stone, and this is an important consideration when buying a stone meant to last a lifetime of daily wear (but other stones are plenty hard enough for engagement ring status).
Some people bring up globally conscious issues, as the environmental and human factors involved in mining diamonds are questioned. However, it is possible to get a conflict-free diamond or a lab-created diamond to assuage some of these concerns.
If these things aren't a concern for you, diamonds are of course gorgeous, and will match just about anything. However there is another serious consideration: price. The cost of a quality diamond is significant. This is something you need to ask yourself about your own priorities: what do you and your partner think is a financial priority? One valid opinion is that an engagement ring is a once-in-a-lifetime, exceptionally meaningful purchase that you will love dearly, wear daily, and even pass down in generations, which justifies a high price. Another valid opinion is that some thousands of dollars could be spent on travel, a down payment, kids, or whatever else and those things are a preferred use of a chunk of change. How you feel is something only you can decide, and don't let anybody guilt you into feeling a different way. It's your ring and your life.
I find it's not always about 'having the money' or not (see Julia Roberts or Meryl Streep with low-key rings), but for many reasons people may have restricted budgets and still want a fabulous ring. If you don't have or care to spend the money on a diamond, there's still plenty of gorgeous out there for you, too.
All that being said, if you want a diamond and it works for you, have at it! On a wedding forum I visit, the fight between diamonds or not gets crazy heated. Remember: it only matters what you chose, not what anyone else chooses. Everyone's reasons and choices are valid for them. Whatever you ring you get, all that matters is that you love it.