Carryover from many common molecular biology reagents can interfere with cluster generation and decrease the quality of your data. Avoiding cross-contamination is also important. A little bit of garbage/unwanted DNA going into the library means MILLIONS of junk sequences coming out of your analysis!
Some tips for getting a "clean" library are: do NOT use ethanol precipitations, do NOT add glycogen or LPA, prewash spin columns (as per their manual) if you are using them. Do not reuse gel box reagents to gel-purify a library, and keep ladder lanes away from library lanes on a gel.
The Core recommends bead cleanups when building sequencing libraries. Illumina kits now use this as the standard cleanup method as well. If you are not using a kit, here is a protocol to follow for library cleanup using AMPure XP beads. Gel purifications may also be used, but we recommend a bead or column wash afterward to ensure there is no carryover of reagents.