I wouldn't expect a guy to ditch his entire wardrobe of graphic tees the minute he turns 21! But I think that gradually, you should start replacing your everyday wear for something more "grown up" - in fact I would give that advice to men and women alike. Even if you are still a student, opting for even a plain shirt or button down dress shirt and a nice crisp pair of jeans (no holes or sandblasting on them) will make you feel more like an adult. You'll feel more confident around people because you look good.
I suggest wearing clothes like that when you are out and about, at school, work, even at the store. When you're at home in the evening or even on the weekends you can wear what you like, including graphic tees. But I guarantee that after awhile of wearing more adult looking clothes, you will wear them ALL the time. It will also be good for you to have a nice suit and tie on hand if you don't already - at your age you never know when you are going to be invited to weddings, graduations, or important family functions. They also look good for big job interviews.
My boyfriend often wears jeans and a simple button down shirt with a plain t-shirt underneath. I'll tell you that it looks clean, sexy, and shows that he cares about how he looks to other people. In the summer he often just wears nice shorts, knee length, with plain t-shirts or short sleeve buttoned shirts. But at home he wears whatever he feels like wearing.
Honestly I think logo t-shirts are fine at 21. It just gets a little odd when I see fourty-year old men in Hollister at the same time as me.. The only thing I think guys should get rid of at that age is the stupid flippy "Bieber" hairdo. That needs to expire when someone turns 17 in my opinion.
fck growing up. wear what's comfortable. I'm 21 and I haven't felt in any hurry to start shopping at banana republic and sell out my youth. cause I mean yeah I work to pay for college and apt, so technically I'm an "adult" but whatever if I wanna wear vans and a shirt with words on it I will! don't rush life. you'll be wearing plenty of 'mature' clothing when your 30.
You can still wear graphic t-shirts and what not, but as you get into your twenties, you should start to add button-up shirts to your wardrobe. Plain, no-logo t-shirts can actually look good, but they look better if they have some kind of texture to them.
Sooner or later, you should add a suit or two as well, or at least wool slacks and a couple of dress shirts and ties (paisley is awesome). For my casual stuff, I mostly go to Eddie Bauer and Men's Wearhouse. For my suits, dress shirts, and ties, I go to Jos. A. Bank (I used to work there as well. They have neat sales all the time).
I think you should rock button downs and nice pair of jeans to go more mature.
I think you should skip wearing graphic T-Shirts most days. Graphic shirts just say "hey look at me" "I just paid to be a walking advertisement" and look tacky in my opinion. I wear plain colored shirts and jeans for casual and if I'm going out I'll throw a golf shirt over my T-shirt. I've had comments from girls saying I dress well. The key to wearing plain clothes and not looking like a bum is wearing shirts, pants, and shoes that go together color wise.