sir, Pls be clear in your perspective. Landsat & has ETM+ sensor, you can follow this link http://www.satimagingcorp.com/satellite-sensors/other-satellite-sensors/landsat/
While downloading please take care that you are downloading Level1 Geotiff products of Landsat datasets. Level 1 Products are orthorectified and have minimum error in Equator and Tropics(ie., Shift of 1 or 2 pixels in worst cases) I don't have idea in higher latitudes.
Even though you have problem with datasets other than USGS, its gonna be a complex one like you have to check Scanning mechanism, orbital corrections etc.
Waheed, like Arun pointed out your question is not very clear. First of all Landsat 7 satellite only had the Enhanced Thematic Mapper Plus (ETM+) Sensor. The Thematic Mapper (TM) sensor was present in Landsat 4 and 5 satellites. So please clarify your question whether you mean ETM+ or TM ? Landsat 7 or Landsat 4,5 ? Can you also attach an image of the shift which you have noticed between the two different images? Which link did you use to download the Landsat Images?
You can use a set of points identifiable in both images to make them match. Depending on the number of points you provide, the precision required and the characteristics of the deformations, you can apply either a similarity, or affine, or polynomial transformation. It is even better if you have points of known coordinates on the field which are identifiable also in the images.
GRASS GIS is an open source GIS alternative which has several LANDSAT-specific tools[1]. GRASS also has a GUI for geo-referencing [2]. It is an alternative to the already mentioned software. QGIs also has a tool you can use [3]