Other Resources:

• Dr. Parmenter's and the Department of Architecture's GIS site contains much information and many links to data, other projects and techniques in ArcGIS. 
• Six year's worth(!) of GIS term projects for  Dr. Maidment's class are linked here.
• Chapters 3 - 7 in the Digital Book "Using ArcGIS Spatial Analyst" are an excellent, highly readable sources of ideas and explanations of the tools available in the Spatial Analyst extension.  There is also sage advice on doing Spatial Analysis.

Some other ideas (now somewhat dated)....

1. Speak with Dr. Sharp about his idea of quantifying unaccounted for recharge to the Edwards Aquifer from the Bull Creek watershed.  This would be a rather simple exercise of delineation higher-order watersheds and calculating their areas, as a start.
2. Cut and fill (volume) calculations using the Spatial Analyst extension, e.g.
   1. What was the volume of glacial lake Missoula, and how much of a difference in volume is represent by different shoreline levels?  Where were dams required?
   2. Where were the spillover points/ice dams for ancestral lake Bonneville for shoreline levels at various heights?
   3. Compare hypothetical (or real) dam sites by potential water storage, land use/land cover impact (how many and how much affected).  Vector and Raster.
      
3. Delineation of landslide-prone areas on basis of slope, soil and/or geology grids.  Use National Park data. Raster analysis.
   
4. Correlation of aeromagnetic anomalies and surface geology and/or topography in tectonically active region.  Raster analysis.
   
5. Least cost path study of routes - e.g. new trails, new roads, pipelines - where topography and geology are principle concerns.  Raster.
   
6. Quantify growth over the last X years on Edwards Aquifer recharge zone in Travis Co using C.O.A. data.  Vector.
   
7. Something with acid mine waste runoff, topography, mine age and type, stream proximity for southwest Colorado (very vague thoughts at this point).  Vector and Raster.
   
8. Build a GIS of your thesis area/area of interest and find something spatially special to do with it.  Raster or Vector.
   
9. Suitability analysis of proposed pipeline route, e.g. Longhorn Pipeline through Austin.
   
10. Use point data of any sort to generate a grid that can be compared to one or more other grids to look for spatial correlations.  E.g. compare chemical concentration data from the US N.U.R.E. dataset to gridded geology to establish link between sinks and sources.  Are particular elements correlated with particular rock types?
    
11. Examine changes in water levels for an aquifer in a region in Texas; quantify volumes and the form of the groundwater table.