I'm in the middle of my 20s so I can't say what else is in store, but so far:
1) School's over. Snap out of it: there's no gold stars anymore. You won't get a grade after everything you do, whether it be in your social or professional life. It might sound shocking, but sometimes I still find myself waiting for the approval of some figure of authority. Make sure you measure your achievements against your goals and not by the opinion of others. After all, you'll be your toughest judge in the end and how you feel about what you've accomplished is what really matters.
2) Life is not a smooth paved road. It's a winding, bumpy, and slightly obscured mountain path. I often feel that we were taught that after college you'd know where you were going and how to get there. There's no set plan, so really take the time to think about what you want in life and what will make you happy. Working slowly, step by step towards something (even if that something is not clear) helps you to discover who you are and what you'd like to do with the rest of your life. And (maybe this goes with out saying) work hard. You might not gain the notoriety or "greatness" you dreamed of when you were younger, but the value of hard work is priceless.
3) Learn to value the friends you have and how to make new ones. Let's face it. As you get older, your social circle seems to shrink and for good reason. It's hard to maintain a relationship, a full-time job, and all the friendships in your life. Friendship loses some of its organic interaction as you become older. It takes a lot of time and effort to make sure you see all the people you care about and make sure that you maintain relationships in a way that is satisfactory to all parties. You also learn to spend the free time with the people who truly care about you and not waste it on those who don't.
4) Take care of yourself. You're not going to look and feel the way you did when you were younger forever. So, start building the habits now to really make sure you take care of your health. Learn to eat better, get enough sleep, exercise regularly, cut out/down on some of your more unhealthy choices and de-stress yourself as much as possible. In the long run, you won't regret it and you'll probably feel a lot better too!
5) Learn to forgive yourself. Everyone's made mistakes and will probably make a whole lot more before the end of their lives. One of the hardest things to do in life is to admit when you're in the wrong, but an even tougher task is learning to forgive yourself. Don't be too hard on yourself. You're going to make mistakes. No one is perfect. Just be honest with yourself, look carefully at what you've done wrong, and then, learn to let it go.
6) Don't judge so much. Form your opinions, but make sure you remember that you're not here to be the judge of everyone and everything. I am a big fan of standing up for yourself and your opinions, but everything in moderation. It's important to learn that not everyone has to agree. You can agree to disagree - that's one of the great beauties in life. Try to keep an open mind and if you're having a tough time with that, just think very carefully before you speak!
7) Have fun - don't forget to live your life. It's easy to get caught up in your 20s with the whole "I'm an adult" mantra and completely throw yourself into work. Don't forget to spend some time on yourself and really enjoy life! We're not on this earth forever and everyone deserves to enjoy the time we're lucky enough to have. So, make sure you let loose once in awhile and appreciate the world around you. More importantly, make sure you can always laugh at yourself and avoid taking yourself too seriously.