What kind of goulash? Are you using cream or sour cream or none? My wife is in Hungary right now and she's having a veal goulash. Good timing on your question because she just e-mailed me the same question today.
I can tell you what I have when in Hungary and what our Hungarian friends serve - whites or reds.
I know, sounds like a wise ass answer but it's not. They generally don't make the same fetish over the pairings that we do in the States. Partly that's because until recently they didn't have the selection, but partly it's because pretty much everyone has a little Olaszrizling growing out back and they made some wine that's in the cellar.
The wines from Hungary are better than ever and there are a few decent ones that are now imported to the US, so you can try some. IMO, a really austere white, like the single vineyard wines from Szepsy and Demeter and Bott isn't as good a match as one with a bit of RS. But that doesn't mean a sweet wine or a late harvest. Just one that's not bone dry.
For reds, we've had Takler's wines from Szekszárd many times with goulash. He has a number and I think he still makes a Kékoportó, or Portugieser, that's pretty good. Has some acidity and it's a relatively light-bodied wine.
Atilla Gere in Villány makes a good Merlot called Solus, and a blend called Kopár Cuvée that's basically a Bordeaux blend and we've had those with goulash but they're a bit big. He also does an Olaszrizling that's a good match.
There were some decent wines from Vylyan in Villány. You may be able to find their Pinot Noir, I know it was imported at one time. And they have a lot of other wines - Belzebub is a blend of Zweigelt, Blaufränkish and I think Kadarka and/or Cab or Merlot. Their wines tend to be somewhat ligher on the oak than some and can be quite good. If you're up in Wisconsin, I think the Konyaris had an importer up there - their Loliense is really quite wonderful and the white is a great match with goulash - it's a blend of several grapes.
If you can find it, try the dry Hárslevelű from Alana. They are a top tier producer and pretty much anything they make is good, some is even great. Or have their dessert wine.