In general, there is two options to identify targets for transcription factors: experimental (ChIP-seq) and sequence-based predictions.
TF binding from experimental data
The are multiple projects that produce binding data of transcription factors and quantify their peaks across the genome. The advantage here is that you know that binding actually occurs, as opposed to motif predictions. But you need the corresponding experiments.
You already mentioned ENCODE, which is probably the biggest producer of such data. NIH's Roadmap Epigenomics is another one, but that focusses less on TFs.
If you have a gene list and would like to know which transcription factor was likely involved, you can do an enrichment test of your gene set in known TF targets. The ChEA (ChIP Enrichment Analysis) database does this.
Prediction using motifs
Another possibility is to look at binding motifs and see whether your gene list is enriched in those. These will, however, be inactive in a given tissue or cell type if the chromatin is packed or the methylation state of the promotor is unfavorable.
Examples for those are the JASPAR and TRANSFAC databases, or the MSigDB motif gene set (as burger mentioned). You can also query those features using the Ensembl genome database (BioMart, REST).
Calculating enrichment in gene sets
Most likely, an analysis you will want to perform is to calculate the enrichment in your gene list, e.g. that you got from differential expression in two conditions.
The most convenient way is to use the Enrichr platform, which is a web page that accepts a gene list and will compute enrichment in ChEA, JASPAR, TRANSFAC, etc. You can also download their gene sets.