When in the workshop, it is important that the woodworker be dressed appropriately. Now, to put your mind at ease, we're not talking about making a fashion statement here. (Personally, I don't think flannel shirts qualify as fashion anyway, but that's just one man's opinion.) What we're talking about is wearing safe Woodworking clothing.
What Constitutes "Safe" Clothing?:
The theme to keep in mind when dressing to go to work in the shop is that your clothes should provide proper coverage, to protect your skin from flying wood chips and debris, and yet be tight-fitting enough so as to avoid getting caught in power tools. Many a gruesome injury can be attributed to a careless worker getting their shirt sleeve caught by a power tool or machine.
Make it a habit to be certain that no part of your clothing is loose enough to get caught up in a power tool.
Dress for the Environment:
While appropriate coverage is vitally important, as clothing can act as a buffer to keep flying wood chips off of the skin, the Woodworking clothing must also be appropriate for the environment. For instance, if you're working outside in Texas or South Florida in mid-August, I wouldn't advise a full, long-sleeved flannel shirt. If you do, you may keep some sawdust off of your skin, but you're going to be stuck to that shirt from all of the perspiration.
Balance is the Key:
The tricky part is to find the balance between keeping your skin covered and dressing for the appropriate environment. You may find that you're perfectly content in a comfortable, well-fitting t-shirt and blue jeans. While your arms are exposed, you'll be much cooler, and you may find the sawdust on your arms is no bother. The point is to work in the relatively tight-fitting attire that you're most comfortable in.
If you're not comfortable, you'll have trouble enjoying woodworking.
Wood Turning Requires Special Attire:
Wood Turning may be the exception to the "wear what's comfortable" axiom. Because so much wood debris becomes airborne from turning, you'll likely want to wear long sleeved shirts and long pants. Additionally, a woodworker's apron and full-face shield are strongly recommended, as you'll be able to deflect most of the debris by donning these two additional items.