Well, there's the
Dazzle HD for $50, though, it only seems to record upscaled picture past 480p. It isn't an absolutely spectacular capture card, but it does what a person needs easily enough. On a budget, you'll be hard pressed to really get something good.
Otherwise, check out the Hauppauge HD PVR's. Not absolutely top of the line, but they spit out some great video and sound quality (my friend owns and uses a Hauppauge 1212 HD PVR all of the time). Most every model does seem to go for about $150 though, so, you know, that might be a deal breaker. Clearly my experience lies in outside devices more than the inner.
Just know that in terms of true HD, you'll have a hard time spending less than about $100, regardless of the type of capture card. Be wary of no-name cards that offer HD, but don't specify available inputs. That can be a red flag that they simply up scale and don't offer what most would consider to be acceptable HD quality. Also, for the love of all that is good, if shopping around on Newegg or something, read customer reviews. Some capture cards may come bundled with an absolutely awful recording software with no alternatives, while others may experience other ridiculous issues while having awful customer support.
I guess the moral of the story is that if you buy an inexpensive capture card, either don't expect true HD, or risk running into a myriad of other issues.