SRAM Cassette with Shimano 105 groupset Can I replace my existing Shimano 12-25 10-speed cassette with a SRAM 11-32 10 speed cassette with no other modifications?
Probably not

If you have a 10 speed 105 group it will be either 5600, 5700 or 5701 series. Looking at Shimano's archived specs from here, 5600 appears in 2006, 5700 in 2011 I believe, 5701 is in the 2014 doc.

The RD-5600 has a max rear sprocket of 27 for both short cage SS and long cage GS versions. The RD-5700 has a max rear sprocket of 28 for both SS and GS versions.  A bigger cassette would likely exceed the total capacity as well unless you have a GS which has a higher capacity for use with triple cranks.

RD-5701 SS has a max sprocket of 30, GS max sprocket of 30 with triple cranks and 32 with double, so if you happen to have 5701 GS double you'd be OK.