• Go to the table browser http://genome.ucsc.edu/cgi-bin/hgTables
• select group "Gene", track "RefSeq", table "refGene"
• click "identfiers: paste list" and copy+paste your list
• output format: CDS fasta
• get output
• Formatting options: unselect everything but "Show nucleotides"
• get output

Normally I would suggest BioMart for this purpose (assuming that your organism is in BioMart) but as I write, it is giving an error. However, here's the procedure for when they fix it:

1. Select MARTVIEW in the top menu
2. Choose database Ensembl genes 64, select dataset for your organism
3. Click Filters, left menu; expand "Gene"; check "ID list limit"; select "Refseq mRNA IDs"
4. Paste or upload IDs
5. Click Attributes, left menu; select "Sequences"; expand "SEQUENCES"; select "Coding sequence"
6. Click "Results", top-left menu.

Currently, this gives the error "Serious Error: Error during query execution: Table 'ensembl_mart_64.ox_RefSeq_mRNA__dm' doesn't exist" - I will report this to BioMart.

If you're willing to try an in-development library, you can try cruzdb. With a script like this:

from cruzdb import Genome
db = Genome('hg19')

refGene = db.refGene

for name in (n.strip() for n in open("names.txt")):
    gene = refGene.filter_by(name=name).one()
    print ">%s" % name
    print "".join(gene.cds_sequence)

and names.txt containing id's like: NM_001127388 NM_001127389

It will create print FASTA file by querying the UCSC genomes database (refGene table), and grabbing sequence from their DAS sequence server.

If you have a long list, see the notes on the cruzdb page about mirroring the MySQL pages locally.