What problem are you trying to solve? The approach and therefore best tools depend on...
- Are you visualising data to (a) analyse it, explore it or open it up, or to (b) communicate a specific, known message about it?
- Who is your audience? In particular, are they (a) casual people who's interest you want to attract (e.g. readers of a magazine, people following a link on twitter, people who work in a related but culturally separate field), or (b) do they have a committed interest in this type of data (e.g. they look at this type of data for a living, or they're a keen fan of this sport...)
If your answer is 1a2a, you have the big challenge of making a data set enticing to casual passers by. Sketch up ideas (maybe with Adobe Illustrator, maybe pen and paper), swot up on or hire skills in interaction design and client-side web programming, then code something up in Raphael.js (my preferred option, works in everything from IE6 to iPads), D3 (great, popular option for proof of concept and prototyping but being purely SVG it doesn't work in IE8 or below, excluding about 40% of people), Processing (viewers must have Java, excludes about 35% of people) Processing.js (HTML 5 Canvas, which can be made to work with IE, and has some benefits, but limits interactivity somewhat), or, if futureproofing isn't an issue and you want to save development time and money, Flash.
If it's 1a2b, your needs are to quickly transform and experiment with data, then show it to people who will be interested. Attracting attention isn't a priority - they're already interested - the key is being able to respond quickly to new questions. Look at stats-y data suites with good visualisation features like JMP, Tableau, R, or if there's no budget and R is too hard, Many eyes, Gephi, or WEAVE.
If it's 1b2a, this is classic infographic design. Get your artist's hat on, and crack out a vector program (design initially in vectors for accuracy and flexibiity) like Adobe Illustrator (which also has basic charting tools), Corel Draw or Inkscape (free) - or, if you've got the time or budget, make an awesome 2D infographic video in Flash or After Effects or an extra awesome 3D video in Blender (free, hard to use), Cinema4D (expensive, moderately hard to use), or Maya (very expensive, hard to use, industry standard).
If it's 1b2b, relax, you're communicating a distinct message to people who are already interested. Speaking clearly and confidently would probably do the trick. Or just give them your Excel file. Or send them an email or PDF with a well designed bar chart or table in it. Don't be too flashy - your audience probably know the nuances of this type of data as well as you do, and they probably don't want a presentational layer between them and their data. Unless it's a complex, unfamiliar data set - in which case, see 1a2a or 1a2b.