Schools typically put together packages with impressive salaries, research budgets, discretionary accounts, and relocation packages -- but that doesn't mean everything has been anticipated at the initial offer. The point of a negotiation is to calibrate a package to fit your unique set of circumstances. If there are things you need to be happy and productive, you should ask for them. In general, it's probably useful to provide a compelling reason. And it goes without saying you're likely to have more luck with detailed, line-item types of requests when it comes to work-related, relocation, and "other" expenses as compared to asking for broad requests that might seem to be pulled out of thin air. Doing research to provide data and evidence that justifies/explains/quantifies your requests may be the obvious "secret" to getting the most from your negotiation.
Provided below is a brief compilation of things you might consider asking for (but that you might or might not get) -- along with some minor tips and commentary. This list is by no means exhaustive, but hopefully it's a starting point for thinking through things that might be useful for your particular circumstances.
Items Listed in the Who Went Where Survey Results
1. Salary (generally hard to move, competitive offers may work, but even then, not always -- probably not the most important thing to negotiate anyway)
2. Summer support (number of years).
3. Compensation for summer teaching (per section basis).
4. Publication bonuses (i.e. cash payment for hits in specified journals).
1. Startup funds. Often this is related to research but might include technology needs, extra discretionary funds, etc.
2. Research budget (e.g. money for recurring needs such as software licenses, databases, paid research participants, RA time, coders, etc.).
3. Conference travel budget (note: faculty registration fees run roughly $500/conference, so update accordingly).
4. Technology budget.
1. Moving expenses (airfare, movers, etc.).
2. Housing trip.
3. Housing support. Depending on circumstances this could include any number of items ranging from access to cheap mortgage rates to downpayment assistance, or perhaps even money to cover expenses related to the sale of an existing home.
Items Not Listed in the Who Went Where Survey Results:
1. Health insurance "gap" coverage (e.g. you graduate in May, your job/health insurance starts in September). This could be either COBRA payments or a separate short-term policy.
2. Student loan repayment assistance.
3. Cash up front to smooth transitions (i.e. signing bonus). Often this is negotiated as 1/9 or 2/9 (and might or might not count as part of your "summer support").
1. Course load reductions (typically one course for the first one to two years).
2. Course development credit (extra release for any new courses developed).
3. Junior sabbatical (one-semester teaching release, pre-tenure).