What are some things that employers can do to foster employee engagement?

Involve employees in the decisions that affect them; customize your programs, policies, benefits, work environments, learning modules, and even compensation to fit their individual (or segmented) needs; give them options, don't force them into a one-size-fits-all solution.

Lauren, employee engagement is the reward organizations get for having all their executives, managers, supervisors, and employees doing their jobs well. To answer your question, start at the top and make sure everyone does their job well.

Lauren,
I believe there are many ways to improve employee engagement. Five categories initially emerge for me although I'm sure there are more:
1. Structural engagement through sharing and asking for input when developing yearly strategic and operational plans, reorganizations, restructuring, relocations, office redecorating, etc., etc.
2. Emotional engagement when involving people with tough messages, business issues that will be difficult to overcome, personal issues that impact the work environment and should be shared, career discussions and planning for the future, etc.
3. Intellectual engagement through involving people in stretching their thinking to improve the way work gets done, explore new technologies, assume new technical roles, etc.
4. Interpersonal engagement by being transparent and sharing your feelings regarding topics, sharing of pertinent information that is legitimately needed for career, performance or business decision making, etc.
5. Social engagement typically done through scheduled office events such as bake sales, fund raising, walkathons, birthday celebrations, anniversaries, retirements get-togethers, sports events, client visits, etc.

Great answers so far. What resonates with me (and seems to be an extension of the above answers) is: "collaborative leadership." Not to say that everything in a company should be democratic. But rather that people's ideas/beliefs/concerns are respected and considered in the decision making process; that employees feel they are valued beyond their functional roles; that discretionary effort is given willingly.

An entrepreneur I interviewed last week explained his measure of success as the organization's leader as: "if the parking lot is still half-full on Friday night at 6pm when there's no deadline to meet."

This is such a great question; and great responses!
Engaging employees indeed is a skill, an art, and takes a unique brand of LEADERSHIP. Im not speaking of the cliche' leadership that dominated the last decade.
True leadership demonstrated by inspiring employees at every level and encouraging growth at all skill levels creates an environment of engaged employees. Succession planning is one of the easiest places to start. Unfortunately, obtaining the buy-in of every "manager" is more difficult than it sounds. (those who are easily threatened by strong leadership below them can stymie even the most well planned program.)
By a company expressing to all employees that the success of the company is dependent on the success of each and every employee, building the leadership and succession plan around the concept that every employee will benefit, and creating the environment in which every employee has the ability to grow, will indeed inspire every employee -- and the result is truly engaged employees at every level within the organization.

Jonathan, a half-full parking lot at 6 pm could mean a lot of overworked employees or many single employees or a group of unhappily married non-drinking employees or that most of the employees come in at 10 am and leave at 6:30 pm. Just joking.

I used to arrive in my office by 7:30 am and leave about 5:30 pm most nights. I then became aware that we had a stampede in from the parking lot every half hour from 7 am to 9 am. We had voluntary staggered working hours to ease the highway congestion. After that I noticed that we had a stampede to the parking lot every half hour starting at 3:30 pm. It wasn't until my MBA studies that I realized I may have been observing the impact of ineffective manage. We were a professional engineering firm but most employees watched the clock.

Thanks for the clarification Bob. Yes, there are other interpretations of that statement, but I don't want to go too far off topic here.

The entrepreneur I interviewed (in research & manufacturing) was commenting on how proud he was of his employees for their commitment and discretionary effort, attributing it to his team's better management. As a comparison he shared that when the company went public, the VC firm brought in their own management team and the parking lot was empty at 5:01pm everyday.

Jonathan, the additional info on the parking is quite instructive, thanks.

Great question Lauren. Let me add my 2 cents to what is already a great discussion here:

From my own perspective, every organisation has its own unique drivers of engagement. Of course, there are trends that research shows. For example, based on Towers Watson's data, we typically find Leadership & Career Development to be strong drivers of engagement. However, these drivers vary - across geographies, across companies.

The way I approach this is first through quantitative analysis to generate some discussion points. You could do this by conducting employee engagement surveys, which measure engagement, and a broad range of factors which affect engagement (performance management, career growth, leadership, core values, alignment, enablement, supervisors etc.). Next, you could use regression analyses to find out which of these various workplace factors influence engagement as an outcome. Typically, you will find 3-4 factors which have a large influence.

Such analyses could be meaningfully used for discussions among HR / Leadership team to identify ways of strengthening employee engagement. Through qualitative discussions on a quantitative analysis could help you to come up with a good way to identify where you should invest time and money.