It goes without saying nowadays that if you're shooting on SD (or even first generation HD gear) that you're seeing your camera show it's age when it's footage is stacked up against the newer models coming out.
Fortunately there are a few excellent options for making the jump to newer HD technology without breaking the bank.
A few notes - all the following cameras shoot at 1080/24p (and other resolution/framerate combos) and record to SDHC cards (tapeless workflows rock BTW)
Without further ado here are some of our favorite budget HD cameras starting with the more traditional HD camcorders:
CANON XA10

Pros: XLR inputs, Dual SHDC slots (allows continuous and dual recording), Small form factor (for discrete shooting)
Cons: Fewer manual settings, menus can be cumbersome to navigate
CANON XF100

Pros: XLR inputs, Better menu and button layout than XA10, manual control of all settings, Excellent image quality for the price
Cons: Single chip sensor, single ring dedicated to zoom, focus and iris
Here's a great in depth review from Philip Bloom on both the XA10 and XF100:
Review of Canon XA10 XF100 XF105 from Philip Bloom on Vimeo.
PANASONIC HMC40

Pros: Least expensive camera with full-manual audio, 3-chip sensor
Cons: 1/4" chips and old image-processing tech can be trouble in low-light, XLR inputs only available by buying separate hotshoe accessory
IF YOU'RE LOOKING TO MAKE A HUGE LEAP IN IMAGE QUALITY THEN A DSLR MAY BE YOUR BEST CHOICE. THESE CAMERAS SHOOT CINEMATIC QUALITY IMAGES BUT LACK THE CONTROL OVER AUDIO LEVELS THAT YOU'RE USED TO SEEING IN A TRADITIONAL VIDEO CAMERA. IF AUDIO IS CRITICAL FOR YOUR PROJECT GRAB AN EXTERNAL AUDIO RECORDER AND RUN DUAL SYSTEM SOUND
CANON 60D

Pros: APS-C Sensor, Same imaging system found in the more expensive 7D, Articulated LCD screen
Cons: No audio input = no monitoring w/ headphones, 12-minute record limit on clips
PANASONIC GH2

Pros: Easy to navigate menus, very low aliasing and moire in images, bitrates up to 176 MB/S (if you're brave enough to patch the firmware), some manual control over audio levels, can accept a dizzying array of lenses by using inexpensive adapters
Cons: No audio input = no monitoring w/ headphones, Micro 4/3 chip creates a 2x crop factor on lenses, slightly noiser than larger chip cameras at high ISO's
At the end of the day it's all about the person behind the camera rather than the camera itself; this being said HD has become the new standard so you've got to keep up with the times.