Whether it's for a pattern in a magazine or yarn company (book contracts are a whole other thing, I'll save that for it's own post!), most of the time you'll be receiving a standard contract. Is there room for negotiation? Usually. Here are a couple of things I've successfully negotiated* in the past:
Say a company offers you $350 for a shawl pattern, you could try asking for $375 or $400. The worst that will happen is they will say no. Just don't come back with "Gee, $350 is a little low, how about $900?" You have to be reasonable. Most of the time, these companies have a budget for their collection or issue. There's a lot of moving parts within that budget, and you are just a small piece of that. If the compensation really is too low for you, don't be afraid to politely decline signing the contract.
Monetary compensation isn't the only thing to consider when looking at a contract. When is the due date? Are you going to be out of the country on vacation or do you have something else due at the exact same time?
Asking for a change to the deadline in the initial contract is much better than having to go to the company a week before your project is due and you have to tell them you need more time. I have successfully negotiated deadlines with magazines in the past. If you ask for an extra week upfront, they might be able to give it you. It's rare that I ask for a change in a deadline when signing a contract, but sometimes you have to ask it. Know your schedule, know what workload you can handle and try to negotiate the due date if you need to (within reason obviously - don't ask to turn in your magazine design two months later than the deadline they are suggesting, they will definitely tell you no).
Remember, this is business, it's nothing personal. If you try negotiating your contract and can't come to an agreement, there's nothing wrong with politely declining. Another opportunity will come along. But like my dad always said, "If you don't ask, you don't get." So don't be afraid to ask for a change if you feel like the contract isn't quite right for you.
*Every company/collection/magazine is different. Sometimes I've asked for more money or a different deadline and received it, sometimes I haven't. Some companies may be open to negotiations, some may not.