If you still want something that acts as a standalone, I have used a few free software options that are pretty good. One disclaimer: the following is all for Windows (since that's what I use). It may or may not be available for other platforms.
The most "straightforward" I think I've come across is DrumTrack by supercoldmilk:
DrumTrack
It's not the most powerful thing on the market, and to be honest I have only used pre-1.0 versions, but it does the basics quite nicely. There's a little bit of a learning curve, but I'm pretty sure it handles the basics (the basics being velocity/volume, tempo, time signature) pretty well.
Keep in mind that it's not 100% functional yet (though again, the 1.0+ alphas might have all the parts in place). However, when I tried it it did allow you to add your own samples to make custom kits.
The one I've come back to after moving away from it (it was buggy) is Hydrogen, which is also available for Linux (and I think OSX):
Hydrogen - advanced drum machine for GNU/Linux
However, the Windows port of it is technically a non-official experimental release:
Hydrogen Forum > Hydrogen on Windows > hydrogen0.9.5_free_setup ( new windows installer )
Hydrogen actually has a few features over DrumTrack, like automatic humanization (for timing and swing as well as velocity). Adding custom kits is a little more complicated, but they're also a bit more powerful (for example, you can set up velocity-dependent layers for each instrument). It's also a more popular program, so some searching should find you some pre-made kits by others.
I don't do a lot of drum programming in general, but when I do, I've had good success with these.
If you're using a DAW that can hoste them, there's also some cool free VSTi plugins (again, Windows-only is possible) that I like:
GTG DP3
GTG DrumSampler I
FrettedSynth SoftDrum (versions exist using samples or Soundfonts)
VirtuaDrum by Angular Momentum
I actually know that most of those aren't available anymore, but you might be able to find them hosted by a third-party freeware plugin site. However, many of those will let you load up your own samples, but they all will come with at least 1 standard set to work with.