Maybe you'd still like to use your lamp in some functional way. Luckily, sturdy lamp bases can be repurposed as bookends, while slender bases look lovely holding candles instead of a bulb. Just gut them of their electrical parts and use as bookends, candlestick holders or other household items.
Be creative and don't be afraid to experiment. For instance, you can try a mosaic pattern or use shellac to attach a series of favorite postcards. Cover the base with old stamps or try a stencil with a bright contrasting color. You can also use a clear lacquer to affix any items to your base.
There's also the option of sewing original covers for your bases, using a new pattern.