With affordable flights to Rangoon (Yangon) courtesy of JetStar Airways, Singapore is second only to Thailand as a launching point for travels to Burma. And if you're considering a visit to Burma now that Aung San Suu Kyi has given the nod to independent travellers visiting, Singapore should be a good spot to get your visa, as it has a Burmese Embassy where you can apply for a four-week tourist visa. BUT only Singaporean citizens or long-term pass holders can apply.
To arrange a tourist visa through the Embassy in Singapore is a little bit complicated and if you're able to get an eVisa or apply elsewhere, that is a preferable option. Tourists cannot apply in Singapore for a visa for Burma (Myanmar).
You're now required to make an appointment via the Myanmar embassy website - the link is near the top right and reads "Online Appointment Reservation for Visa Service". Click there and select a day that works for you - note the days fill up fast, so leave yourself some wiggle room. You then need to fill out the online form which includes you needing to upload a scanned image of your passport photo.
Once submitted and approved, the embassy will email you an application form and you'll be required to show up at the embassy on the agreed day between 08:00 am and midday to fill out the form they sent you and supply two more passport photos. Yes, we know, you already did this online.
You then return that afternoon (04:30pm to 05:30pm) to pick up the visa.
A tourist visa costs S$35.
There is a good write-up of a firsthand visa application (by a Malaysian traveller) here. Though it predates the online appointment thing.
The Embassy of the Union of Myanmar is located at 15 St. Martin's Drive, within walking distance of Orchard Road MRT station. Office hours are Monday to Friday, 9:00 – 13:00 and 14:00 – 17:00. Questions can be directed to (65) 6735 0209 or firstname.lastname@example.org. http://www.mesingapore.org.sg/visa.html