Disclaimer: I claim no ownership of any resources listed below. I have copied a few of them onto this site for your convenience. There is a link to the source on each page that I copied.
Rocket Calculator
This is a little program that will tell you the best way to build a rocket for the requirements that you set it. Build yourself a payload, then tell it how far you need to take it (in dv).
Visit the site.
Delta-V Map 1
I like this map better. It shows the total delta-V needed to reach any destination, as well as the amount of dV used by each leg of the journey. Unfortunately, round trips don't seem to be pre-calculated, but half the work has still be done for you.
View my copy.
Delta-V Map 2
This is another map for those who don't like the first one. The formatting is still nice and clean, but there's just something that looks nicer about Map 1 to me. Feel free to check both and see which one you like better.
View my copy.
Interactive Delta-V Planner
This interactive planner lets you click on starting and ending locations, and shows you how much dV is required to reach that destination. Be warned, however, that aerobraking around any planet whose atmosphere is at least as dense as Kerbin's probably can't bring you safely from super-orbital speeds. Some fuel usage will be required, without large heat shields.
Visit the Site.
How do I get there?
If you're struggling to figure out the correct launch angle to get from LKO to another planet, this is the resource for you. It shows you ejection angles, and what angle Kerbin should be relative to your destination. You can even choose to start at other planets if you prefer.
Visit the Site.
When should I launch?
This resource has you plug in the earliest date you can launch, and then spits out the next optimal window to reach whatever planet you tell it you need to reach, complete with a generated chart to show you how your dV usage would change if you launched at a different nearby time.
Visit the Site.
Visual Airplane Guide
This is a very well-written guide to building airplanes. The copy that I have here has been chopped up into smaller pages, and has the innacurate bits removed that related to Kerbin's atmosphere (which as of 1.0 is much more realistic than it was during the time of the guide's writing)
View my copy.
Manley's Tutorials
Scott Manley is a genious Kerbonaut. He's well regarded among the KSP community, and has dozens of videos available to help you learn how to play the game effectively. Be wary of older tutorials. The physics has changed significantly since previous versions, so older designs and launch profiles may not work as expected.
Visit the Site.
Von Kerman's Rocket School
Another resource that, upon my brief viewing, has lots of great, if outdated, youtube tutorials. Check this out to learn the thought process behind building great rockets for specialized and specific purposes.
Visit the Site.
m_sporkboy's Mun Lander Guide
Reddit's m_sporkboy has created a wonderful guide to creating effective Mun landers. Check it out.
Visit the Site.
jelliestjellyfish's Checklists
Reddit's jelliestjellyfish has created some very extensive and useful checklists. If you're getting stumped by frequently forgetting something, or even just plain not knowing that some parts are useful for a ship, these checklists can be very useful.
Visit the Site.
PhildeCube's KSP Career Mode for Absolute Beginners
Phildecube is a frequent contributor to reddit.com/r/kerbalspaceprogram, and has created a great guide to a very efficient way for new players to get started in career mode. Some contracts are just not worth doing. This guide can help you decide which, not to mention helping you figure out some early game rocket designs that simply work.
Visit the Site.
Kerbal Maps
Kerbal Maps is a website that gives you access to maps of every body in the Kerbol system (that's the star system that Kerbin is part of). It's a great resource for trying to pick a nice place to land, or for comparing the game's coordinates with visual locations.
Visit Site.
Flappy Space Program
Flappy Space Program is just a small game. Click madly to get little birdy things into orbit around a super tiny planet. Get as many birds in orbit as you possibly can. Because it's 2-D, collisions are very likely. It's a fun little time waster.
Visit the Site.